CFE National 4 - Pack 3 · Pegasys 2013 Use numerical skills to solve straightforward real – life...
Transcript of CFE National 4 - Pack 3 · Pegasys 2013 Use numerical skills to solve straightforward real – life...
Pegasys 2013
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CFE National 4 - Pack 3
Unit : Numeracy (NUM)
WORKSHEETS
Worksheets covering all the unit
topics
+ Answers
Pegasys 2013
INDEX NUMERACY
Use numerical skills to solve straightforward real – life problems involving
money/time/measurement
Selecting and using appropriate numerical notation and units
Selecting and carrying out calculations
Reading measurements using a straightforward scale on an instrument
Interpreting the measurements and results of calculations to make decisions
Explaining decisions based on the results of measurements or calculations
Interpret graphical data and situations involving probability to solve,
straightforward real-life problems involving money/time/measurement
Extracting and interpreting data from at least two different straightforward
graphical forms
Making and explaining decisions based on the interpretation of data
Making and explaining decisions based on probability
Pegasys 2013
Use numerical skills to solve straightforward real – life problems involving
money/time/measurement
Four Rules
1. Copy and complete the following sums:
2. (a) Find the sum of 245 + 567 + 7382
(b) What is the difference between 2637 and 1795?
3. In Notlimah High School there are the following number of pupils in S1 – S4.
S1 - 340
S2 - 371
S3 - 296
S4 - 254
How many pupils is this altogether in S1 – S4?
4. The Smythes set out on a journey of 234 miles. After they have travelled 147miles they
stop for a break.
How many kilometres do they still have to travel?
5. At four shops Fiona spends the following amounts: £14.78, £7.45, £5.10 and £10.54.
(a) How much did Fiona spend altogether?
(b) How much did she have left from £50?
(a) 2 5 6 5 (b) 7 3 6 3 (c) 2 5 7 (d) 8 5 7 3 6
+ 7 2 9 7 – 2 5 7 8 × 8
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6. If it costs £8.60 to hire a bike for a day, how much would it cost to hire it for
the whole of the month of June?
7. Find the total cost of : 3 tee shirts at £12.75
5 jumpers at £27.50
4 tops at £22.40
1 coat at £87.40
8. Sanjay earns £12 a day. How much will he earn in a year when he works 312 days?
9. 780 pupils in a school have to be put into classes of 30.
How many classes would there be?
10. Jotters come in packs of 25. If the Maths
Department need 1600 jotters, how many packs should they order?
11. A can of juice costs 30p.
(a) How many cans could be bought for £1.30.
(b) How much money would be left over?
12. A netball team consists of 7 players.
(a) How many teams can be formed from 60 people?
(b) How many would have to sit out?
13. A gardener has 329 plants which he wants to put in rows of 12.
How many rows will he plant and how many plants will be left over?
14. Mrs. Mackay bought a packet of tea costing £3.47and a packet of sugar costing 98p.
How much did she spend altogether?
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15. Margaret gets £25 a week for pocket money. She spends £14.65 on bus fares, £4.75 on
sweets and she saves the rest.
(a) How much does she spend on bus fares and sweets?
(b) Margaret is saving up to buy a new bike which costs £187. How many weeks will it
take her to save enough to buy her bike?
16. Stewart has £50 to buy some presents. He is going to buy a computer gamecosting £15.99,
a book costing £12.75 and some perfume costing £22.40.
Does he have enough money to buy all of these?
17. Tommy is buying a new television. He cuts out a voucher from a newspaper
which is offering a discount of £75 on it.
Tecom is selling the television for £640.
How much would Tommy actually pay using his voucher?
18. The local DIY store was charging £15.50 for a 2-litre can of paint. In a sale they were
selling it for £12.95.
How much discount was this?
19. A pair of shoes cost £42.70 in a sale after£12.30 had been given as a discount.
How much were the shoes before the sale?
20. Sunita wants a new bike. The shop was offering a discount of £45 on it.
The full price of the bike was £176.
How much did Sunita actually pay for her bike?
21. James saw an advert in the paper for a holiday in Paris. It cost £235 per person
but the travel agent was offering it for £170 per person as a last minute deal.
James decided to take his girlfriend.
How much did he save altogether on the two packages?
22. A school got a discount of £250 on the full price of jotters. They paid £840 for them.
How much were they before the discount was given?
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23. The full price of a computer in Computer world was £500 and in World of Computers
was £555 with a discount of £60offered.
Which shop was the cheaper and by how much?
24. A school bought some calculators which cost £74.20. This included£10.20 VAT. How
much will the calculators actually cost the school if there was no VAT charged?
25. In a "Special Offer" a washing machine is being offered "without VAT".
The price is £336 but Jean only pays £280.
How much VAT was included before the offer?
26. Claire bought 12 large bottles of "Loca" for a party. They cost £1.19 each .
How much did she pay altogether?
27. It cost Elsie £34.80 to buy 8 Easter eggs for her friends. How much was this for each one?
28. 35 people were going ten-pin bowling. It cost each person £5.50 for 2 games.
How much did it cost altogether for the 35 people?
29. For her birthday, Naaila took her 4 best friends to the cinema and then to Le Hut de Pizza.
The total cost of the outing was £44.75. How much was this for each person?
{CAREFUL!}
30. 6 friends had a day out to the seaside. They all had ice cream which cost £1.45each.
Two had a pizza costing £8.25each, three had a fish supper costing £6.30 each and the
sixth one had a burger costing £5.49.
(a) Calculate the total cost of the day out.
(b) They decided to each put £8 in a "kitty". Was this enough to pay for everything
they had?
(c) How much over or under were they?
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31. Derek bought a house for £23000 and spent another £7000 doing lots of repairs to it and
then sold it for £36000.
How much of a profit did he make?
32. Julie is a florist and makes up floral gifts to sell for charity.
It costs 85p to make each one and Julie sells them for £1.50.
(a) How much profit does she make on each one?
(b) She sold 150 altogether. How much did Julie make for charity altogether?
33. The school tuck shop bought a box of 48chocolate bars which cost £15.36.
They were sold for 40p each.
How much profit was made if all the bars were sold?
34. A few years ago it cost £1.50 to buy a share in an enterprise company.
(a) Sara bought 250 shares. How much did they cost her?
Nowadays they are worth only £1.25 each.
(b) How much in total has Sara lost on her 250 shares?
35. Bernie was making a patio in his back garden. He bought 50 slabs which cost him a total
of £175.
He only used 42 of them and sold the rest to a friend for £3 each.
How much did he lose on each of the slabs he sold to his friend?
36. 10 people go out for a meal. The total bill for the meal is £231.
How much is this for each person?
37. The cost of entry to the Home Show was £6.50 for adults and £4.50 for children.
How much would it cost Barry to take his wife and 2 children?
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38. Anna gets paid £16 464 each year and gets it in 12 equal amounts.
How much does she get each time?
39. Steven is tiling his kitchen and needs 435 tiles.
The tiles come in boxes of 25.
(a) How many boxes of tiles would he need?
(b) How many tiles would Steven have left over?
40. Linda is going to the ‘Don’t Get Fat’ club to try to lose some weight. Her starting weight is
564kg.
This table shows her progress card for the first few weeks:
Complete the table to show Linda’s progress.
41. David wants a new bike that costs £216.
His Mum gives him £108 and he saves up the rest from his paper round.
If he manages to save £9 a week, how many weeks will it take him to get
his bike?
Week Number Lost Gained Weight
1 23kg
2 16kg
3 04kg
4 09kg
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42. At the seaside three friends have a game of crazy golf. Here are their scores:
Who won the game?
43. Here are the prices of several items in the local chemist:
Shampoo: £2.35
Deodorant: £1.87
Shower Gel: £2.75
Shaving Foam: £2.24
Toothpaste: £0.97
Handwash: £1.24
(a) Adrian buys shampoo, deodorant and toothpaste.
How much does it cost him altogether?
(b) The next week there is a special offer:
How much would the same three items have cost Adrian now?
44. A section of the Clyde walkway is 17km long. Kashef and his friend walked different parts
of it on three different days. On day 1 they walked 5·73km and on day 2 they walked
4∙05km.
(a) How far did they walk altogether over the two days?
(b) If they walked the remainder of the 17km on day 3, how far did they walk on that
day?
Buy 3 items and get the cheapest one free!
Hole
Number 1 2 3 4 5 6 7 8 9
Polly 3 5 4 7 1 3 3 3 4
Wally 2 4 6 8 2 3 2 4 1
Doodle 3 5 1 4 4 5 6 3 6
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Add and Subtract positive and negative numbers
1. Calculate :
(a) 3 + (2) (b) 3 + (2) (c) 6 3 (d) 4 + 4
(e) 5 + 7 (f) 9 2 (g) 7 3 (h) 8 + 2
(i) 10 + (5) (j) 2 + (4) (k) 12 + (7) (l) 4 + 8
. (m) 3 + 2 (n) 5 + (8) (o) 8 + (7) (p) 4 5
2. Calculate
(a) 20 30 (b) 70 + (20) (c) 50 + 10 (d) 30 40
(e) 18 + 8 (f) 35 40 (g) 27 15 (h) 21 + (37)
(i) 12 35 (j) 13 + 49 (k) 15 + (15) (l) 130 200
(m) 37 + 14 (n) 58 85 (o) 19 52 (p) 72 + (17)
3. The temperature in Glasgow was 7ºC. The temperature in Oslo was 11 degrees lower.
What was the Oslo temperature?
4. My bank balance was –£25. I paid in £20 my aunt gave me for my birthday.
What is my new balance?
5. When a plane took off the outside temperature was 14oC . By the time it had climbed to
30000feet, the outside temperature was –45oC.
By many degrees had the temperature fallen?
6. Freezers operate at different temperatures depending on their star ratings. A 1 star freezer
operates at – 6oC and a 2 star at – 12
oC.
What is the difference in the operating temperatures of these two freezers?
7. A year such as 123BC can be thought of as 123 and one such as 2003AD as +2003.
The Roman Emporer Tiberius Caesar Augustus was born in the year42BC and died in the
year 37AD. How old was he when he died?
8. Put the answers to these calculations in order starting with the smallest.
A – 12 – (–2) B – 3 + 13 C – 5 + (– 6)
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Percentages
1. Littletrees department store is offering discounts of 10% to customers who take a store
card. Calculate the cost of items which cost the following amounts before discount:
(a) £50 (b) £100 (c) £25 (d) £30
(e) £95 (f) £10 (g) £200 (h) £150
(i) £230 (j) £890 (k) £275 (l) £184
(m) £99 (n) £67 (o) £23 (p) £128
2. The Carillon Call Company is giving a 15% loyalty discount to telephone customers.
Calculate the cost of these bills after the discount is applied:
(a) £70 (b) £25 (c) £98 (d) £43
(e) £120 (f) £50 (g) £77 (h) £114
(i) £76.80 (j) £92.60 (k) £55.20 (l) £136.40
(m) £22.20 (n) £35.40 (o) £62.80 (p) £100.60
3. CutscoCash’n’Carry charge VAT at the rate of 20%. Calculate the VAT due on goods
costing :
(a) £100 (b) £30 (c) £50 (d) £70
(e) £250 (f) £180 (g) £90 (h) £400
(i) £82 (j) £76 (k) £94 (l) £138
(m) £104 (n) £222 (o) £68 (p) £36
4. Calculate the final cost of these bills at the CutscoCash’n’Carry
(a) £100 (b) £50 (c) £80 (d) £30
(e) £45 (f) £250 (g) £700 (h) £2000
(i) £10000 (j) £170 (k) £283 (l) £49
(m) £139 (n) £22 (o) £1995 (p) £7.50
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VAT
The rate of VAT is currently 20%.
1. A docking system costs £240 plus VAT. How much would have to be paid for it?
2. In the Carry and Cash, Pauline boughta box of chocolate bars. The price tag said £12.60
plus VAT.
How much did Pauline actually pay for her chocolate bars?
3. Copy and complete this electricity bill:
Cost of electricity: = £ 360
VAT: = £
Total : =
4. Copy and complete this Gas Bill:
Cost of gas: = £83.50
VAT: =
Total: =
5. A school bought some calculators which cost £74.20 plus VAT.
How much will the calculators actually cost the school?
6. A washing machine is being offered for £329 plus VAT. Calculate the price of the
washing machine after VAT is added.
Pegasys 2013
More Percentages
1. Find: (a) 25% of 40 (b) 10% of 780 (c) 20% of 55
2. In a quiz there were 60 questions altogether:
Team A answered 20% of the questions correctly
Team B answered 25% of the questions correctly
Team C answered 50% of the questions correctly
How many questions did each team answer correctly?
3. 75% of the pupils in a school do not attend on the last day before a holiday. If there are
1244 pupils in the school, how many did attend on the last day?
4. Find the following amounts:
(a) 45% of £450 (b) 23% of £236 (c) 78% of £890
5. During a period of 55 minutes a pupil spent 15% of the time day dreaming. How many
minutes is this?
6. A packet of crisps weighs 30g. Special offer packs give 40% extra free. What weight of
crisps do you get in a packet now?
7. Susan was buying a new computer. She had to pay a deposit of 30%.
How much deposit would have to pay if her computer was going to cost £900?
8. In a sale, a bike which normally costs £290 is being offered with a 24% discount. How
much would be paid for the bike after discount?
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9. The local sports shop is having a sale and offering the reductions shown in the diagrams.
Calculate the ‘sale’ price of each item.
(a) (b)
(c)
10. In a group of 240 pupils 50% of them said they enjoyed Maths.
How many pupils was this?
11. In a special offer in the supermarket a packet of soap powder was offering
‘20% EXTRA FREE’.
The packet normally weighs 700g. How much extra would you receive?
12. (a) At a Halloween disco there were 160 pupils.10% of them were dressed as witches,
25% as ghosts and the rest as something else.
How many were not witches or ghosts?
(b) 75% of them took a turnip lantern. How many turnip lanterns were there?
(c) 20% of the pupils didn’t dance. How many did dance?
Badminton Racquet: £30
Discount: 20%
Ice Skates: £45
Discount: 10%
Skis: £256
Discount: 25%
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Percentages again
1. The table below shows Gianni’s test scores for his school subjects.
(a) Express each score as a percentage.
(b) In which subject did he do best?
2. What percentage is
(a) 19 of 76 (b) 54 of 60 (c) 15 of 25 (d) 28 of 80
(e) 84 of 168 (f) 56 of 160 (g) 126 of 180 (h) 72 of 180
(i) 63 of 315 (j) 126 of 280 (k) 54 of 360 (l) 108 of 150
(m) 176 of 320 (n) 5 of 50 (o) 60 of 75 (p) 48 of 192 ?
3. Calculate the percentage profit (as a percentage of the cost price) on the following
(a) cost price : £75 (b) cost price : £24
selling price : £90 selling price : £30
(c) cost price : £180 (d) cost price : £ 17.60
selling price : £ 198 selling price £24.64
(e) cost price : 10p (f) cost price : 50 p
selling price : 12p selling price : 52p
4. Mrs. Patel buys 12 light bulbs at the supermarket. When she gets home she finds that 3
of them are faulty. What percentage are faulty?
5. In a class survey it was found that 27 out of the 30 pupils in the class were wearing full
uniform. What percentage of the class were wearing full uniform?
English Maths French History Biology Craft Physics Art
score 42 22 60 16 21 45 18 36
out of 50 25 75 20 25 60 30 40
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6. Chris is driving to London, a distance of 640 kilometres. What percentage of his journey
has he covered when he has driven 416 kilometres ?
7. Donna gets £7.50 per week in pocket money. She wants to buy a magazine costing £3.60.
What percentage of her pocket money is this?
8. In a school of 720 pupils, 396 are boys.
What percentage are girls?
Pegasys 2013
Fractions, Decimals and Percentages (1)
1. Calculate:
(a) 3
1 of £96 (b)
5
1 of 65kg (c)
7
1 of £36.40
(d) 4
3 of 48cm (e)
8
5 of £136 (f) 8
7 of 58·4g
(g) 3
2 of £15.96 (h)
10
9 of 45kg (i) 7
3 of £10.92
(j) 6
5 of £5.10 (k)
8
3 of 984mm (l)
4
3 of £1.08
(m) 20
11 of £2540 (n)
16
9 of 480tonnes (o)
17
5 of 25·5kg
2. Calculate :
(a) 26% of £90 (b) 54% of 300g (c) 13% of £45
(d) 42% of 60kg (e) 17% of £10 (f) 21% of 85cm
(g) 27% of £64 (h) 5% of £340 (i) 65% of £880
(j) 8% of 4500g (k) 80% of £250 (l) 94% of £360
(m) 78% of £1500 (n) 4% of £12 (o) 7% of 1200tonnes
3. Calculate each of the following rounding your answers to the nearest penny:
(a) 36% of £13.20 (b) 24% of £12.71 (c) 1% of £6.35
(d) 47% of 89p (e) 57% of £10.43 (f) 41% of 51p
(g) 12% of £18.30 (h) 4% of £341.20 (i) 5% of £834.65
(j) 81% of £3.45 (k) 9% of £2.57 (l) 34% of 88p
(m) 71% of £1.53 (n) 3% of £12.08 (o) 57% of 97p
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4. Change each of the following fractions to percentages. (Round your answer to the nearest
percent when necessary)
(a) 5
4 (b)
4
3 (c)
25
7 (d)
10
7 (e)
100
17 (f)
20
19
(g) 9
5 (h)
11
3 (i)
25
18 (j)
12
5 (k) 8
1 (l)
13
8
(m) 15
1 (n) 7
3 (o)
31
6 (p) 365
38 (q) 95
48 (r)
29
6
5. John's schedule marks are shown in the table below:
(a) Copy and complete the table by calculating John's "percentage mark" for each
subject.(Round each answer to the nearest percent where necessary).
(b) Which was John's best subject?
(c) Which was his worst?
Subject Maths English Tech Science Art History French
Mark 45 out of 60 64 out of 72 40 out of 65 38 out of 55 75 out of 90 27 out of 40 63 out of 95
%
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Fractions, Decimals and Percentages (2)
1. Increase each of the following by 15%.
(a) £250 (b) 160kg (c) 25cm (d) £36
(e) 2100g (f) 210oC (g) £8 (h) £3500
2. Decrease each of the amounts in Q1 by 20%.
3. The nine workers in a small factory are given different percentage wage rises dependant
upon their length of service. The table below represents their weekly wages.
Copy and complete the table below:
Name Old Wage % Increase Increase New Wage
John Hughes £230 4% £9.20 £239.20
Steven Higgins £168 6%
Susan Marshal £210 4%
Stewart Aitken £145 2%
Pamela Grant £360 3·5%
Neil McShane £225 6%
James Mackie £235 8%
Lorna Graham £210 4·5%
Pat Lavery £468 5%
4. For each diagram below, write down (i) the fraction shaded; (ii) the percentage shaded
.
(a) (b) (c) (d)
(e) (f) (g)
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5. Calculate the fraction and percentage of vowels in each word below.
(a) (b) (c)
6. (a) In a class of thirty pupils, 6 were absent. Calculate the percentage absent.
(b) A machine produces 300 heating elements in a morning. Six are found to be
defective.
What percentage of the elements are defective?
(c) A small farm has 160 sheep. During a severe storm the farmer loses 8 sheep.
What percentage of the sheep got lost?
Pegasys 2013
Fractions, Decimals and Percentages (3)
1. VAT is charged at 20%. Calculate the VAT on each item below.
(a) A stereo costing £230 (b) A fridge costing £148
(c) A cooker costing £456 (d) A watch costing £68
(e) A computer costing £650 (f) A gold ring costing £134
2. Find the total cost of each item in Q1 after the VAT has been added.
3. A man places £2300 in a savings account which has an annual interest rate of 4%.
(a) How much interest will he earn in the first year ?
(b) Assuming he does not touch his money, how much does he now have in the bank
at the beginning of year two?
(c) Hence calculate the interest he will get at the end of year two.
4. A woman places £22100 in a Post Office savings account which has an annual interest rate
of 5%.
(a) How much interest will she earn in the first year?
(b) Assuming she does not touch her money, how much does she now have in the bank
at the beginning of year two?
(c) Hence calculate the interest she will get at the end of year two.
5. Steven places £800 in a Building Society at an annual interest rate of 3%.
How much will he have in his account after two years?
6. Susan invests £800 in a Building Society at an annual interest rate of 6%.
How much will she have in her account after two years?
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Fractions
1. Find: (a) 2
1 of £30 (b) 3
1 of £96 (c)
4
1 of £20
(d) 5
1 of £230 (e)
10
1 of £324 (f)
6
1 of £36
2. Work out the answers to:
(a) 2
1 of 420cm (b) 4
1 of 3320 ml (c)
6
1 of £564
3. A piece of wood is 8·4m long. 3
1of it is used.
How many metres are used?
4. On board a ship there has to be someone 'on watch' all the time. Each
person is on duty for 41 of a day. How many hours is this?
5. In the cinema there are 230 people. 10
1of them are children.
How many adults are there?
6. There are 8 people in a rowing team. 4
1of them are girls? How many boys are there
in the team?
7. In a basket there are 24 Easter eggs. 4
1of them are milk chocolate,
3
1of them
are dark chocolate and the rest are white chocolate.
How many white chocolate eggs are there?
8. Anne is going to be 16 on her next birthday.81 of the candles on her cake are
green, 21 are red and the rest white.
How many white candles are there?
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9. In Killiber High School there are 252 pupils in third year. On the last day of term
only 7
1 of them were in school.
(a) How many pupils were at school?
(b) How many were absent?
10. A film lasts for 2hrs and 30mins. After I had watched 5
1 of it I fell asleep. How many
minutes of the film did I see before I fell asleep?
11. On 6
1 of the days in June this year there was some rain.
On how many days was it completely dry?
12. In the course of a day most of us spend 3
1 of it asleep.
For how many hours each day are we awake?
More fractions
1. Find the following:
(a) 4
3 of 256 m (b)
5
2 of £400 (c)
8
5 of £308
2. There are 48 sweets in a packet. 4
3 of them are citrus flavours.
How many citrus sweets are there in the packet?
3. In a class of 24 pupils 8
7 of them are present.
(a) How many pupils are present?
(b) How many are absent?
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4. In a school there are 1450 pupils. 5
4 of them bring a mobilephone to school.
(a) How many pupils bring a mobile phone?
(b) How many do not bring a phone with them?
5. In a box of 36 chocolates, 9
4 of them are milk chocolate,
3
1 of them are white chocolate
and the rest are dark chocolate.
(a) How many are milk chocolate?
(b) How many are white chocolate?
(c) How many are dark chocolate?
6. There are 100 pencils in a box. 5
3 of them are plain.
8
3 of the remainder have rubber tips
and the rest are coloured.
(a) How many plain pencils are there?
(b) How many rubber-tipped pencils are there?
(c) How many coloured pencils are there?
7. 7
5 of the cars in a car park were grey. If there were 560 cars altogether, how many
of them were grey?
8. Daniel was building a jigsaw which had 600 pieces in it. If he had fitted in 12
5 of
the pieces, how many had he still to fit?
9. In a box of 36 coloured pencils, 9
2 of them were shades of red. How many were not
shades of red?
Pegasys 2013
ROUNDING – revision and 2 decimal places
1. Round to the nearest unit:
(a) 2·9 (b) 5·6 (c) 1·4 (d) 8·3
(e) 7·7 (f) 3·1 (g) 4·5 (h) 9·2
(i) 2·12 (j) 7·93 (k) 6·25 (l) 1·09
(m) 4·76 (n) 8·45 (o) 3·93 (p) 5·55
3. Round to the nearest unit:
(a) 12·4 (b) 35·1 (c) 27·6 (d) 82·7
(e) 17·9 (f) 38·2 (g) 36·3 (h) 90·2
(i) 123·1 (j) 563·8 (k) 18·5 (l) 343·3
(m) 44·87 (n) 218·34 (o) 73·82 (p) 119·18
3. Round to the nearest ten:
(a) 23 (b) 74 (c) 68 (d) 85
(e) 57 (f) 31 (g) 15 (h) 94
(i) 62 (j) 75 (k) 16 (l) 49
(m) 33 (n) 82 (o) 71 (p) 34
4. Round to the nearest ten:
(a) 213 (b) 128 (c) 761 (d) 344
(e) 275 (f) 119 (g) 515 (h) 202
(i) 112 (j) 563 (k) 136 (l) 499
(m) 431 (n) 184 (o) 256 (p) 314
5. Round to the nearest hundred:
(a) 270 (b) 150 (c) 340 (d) 830
(e) 725 (f) 384 (g) 451 (h) 919
(i) 111 (j) 252 (k) 666 (l) 715
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(m) 545 (n) 186 (o) 237 (p) 809
(q) 1265 (r) 1354 (s) 2136 (t) 3456
(u) 1881 (v) 1999 (w) 6543 (x) 8129
6. Round each number to i. the nearest ten
ii. the nearest hundred
iii. the nearest thousand:
(a) 2911 (b) 5667 (c) 1459 (d) 8321
(e) 7774 (f) 3103 (g) 4518 (h) 9286
(i) 2125 (j) 7932 (k) 6253 (l) 1094
(m) 4768 (n) 8451 (o) 3939 (p) 5999
7. Round the following numbers to 1 decimal place:
(a) 0·31 (b) 0·29 (c) 0·56 (d) 0·61
(e) 0·22 (f) 0·18 (g) 0·37 (h) 0·26
(i) 0·94 (j) 0·43 (k) 0·75 (l) 0·68
(m) 0·86 (n) 0·24 (o) 0·73 (p) 0·99
8. Round the following numbers to 1 decimal place:
(a) 2·91 (b) 5·68 (c) 1·47 (d) 8·33
(e) 7·75 (f) 3·11 (g) 4·52 (h) 9·26
(i) 2·12 (j) 7·93 (k) 6·25 (l) 1·09
(m) 4·76 (n) 8·45 (o) 3·93 (p) 5·55
9. Round the following numbers to 1 decimal place:
(a) 62·035 (b) 15·619 (c) 31·475 (d)
18·303
(e) 47·275 (f) 0·123 (g) 10·542 (h) 39·626
(i) 20·818 (j) 0·2938 (k) 61·465 (l)
1·0094
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(m) 49·869 (n) 8·4011 (o) 17·995 (p)
0.·987
10. Round the following numbers to 2 decimal places:
(a) 2·915 (b) 5·663 (c) 1·408 (d) 8·321
(e) 7·761 (f) 3·115 (g) 4·526 (h) 9·212
(i) 2·128 (j) 7·937 (k) 6·254 (l) 1·092
(m) 4·763 (n) 8·451 (o) 3·938 (p) 5·503
11. Calculate the following and give your answer correct to 2 decimal places.
(a) £37 is shared among 6 people. How much does each person get?
(b) Eggs cost £1.90 a dozen. How much does it cost for one egg?
(c) Jan can run 90 m in 96 second. How long does it take her to run 1 m?
(d) Karen drives 400 miles in 7 hours. How far does she drive in 1 hour?
(e) A printer can print 377 pages in 1 hour. How many does it print in 1 minute
(f) Granny Smith left £967 in her will, to be shared among her 7 grandchildren.
How much will each receive?
(g) A photographic company charges £3.99 to develop 24 photographs.
How much does it cost for 1 photograph?
(h) Chris took 3 ½ minutes to complete 4 laps of the go-cart racing track.
How long did it take him for 1 lap?
(i) 15 videos on a shelf take up 44 centimetres of shelf space.
How much space does one video take up?
(j) It takes me 44 minutes to cycle 16 km. How far can I cycle in 1 minute?
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FURTHER ROUNDING
1. Re-write these sentences giving the measurement to the nearest unit:
(a) Ahmed measured the length of his lounge to be 43 metres.
(b) The height of the Eiffel Tower is 32375 metres high.
(c) The tallest man in the world is 2895 centimetres tall.
(d) The longest fingernails ever grown measured 48434 cm.
2. Measure the heights of these pictures giving answers to the nearest centimetre.
(a) (b)
(c)
3. Round each of these amounts of money to the nearest penny:
(a) £2.4624 (b) £90.276 (c) £32.4053 (d) £86.899
4. Do these sums on your calculator and write down your answers rounded to the nearest
penny:
(a) £23.21 5 (b) £573.86 9 (c) £5.56 6 (d) £258 7
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Answer these questions to the nearest penny.
5. Darren bought 4 oranges in a pack which cost him £1.53.
How much is this for each one?
6. At a funfair there is a special ticket which allows you to have 12 turns on
the roller coaster. The cost of this ticket is £22.
How much is this for each turn?
7. A weekly pass for the bus costs £15.25. Callum uses the pass to travel to work every day
for a full week.(7 days)
How much does it cost him per day?
Weekly pass
£1525
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ROUNDING – Significant figures
1. Round to 1 significant figure:
(a) 23 (b) 5·5 (c) 78 (d) 31
(e) 125 (f) 309 (g) 291 (h) 843.6
(i) 7646 (j) 1928 (k) 8003 (l) 5192·7
(m) 10·9 (n) 556·2 (o) 3·98 (p) 12345
(q) 1·01 (e) 93 (s) 0·86 (t) 606
2. Round to 2 significant figures:
(a) 8·72 (b) 92·8 (c) 0·186 (d) 679
(e) 2·112 (f) 6·463 (g) 31·4 (h) 25·8
(i) 24·27 (j) 18·76 (k) 6397 (l) 4·99
(m) 0·0526 (n) 0·00613 (o) 0·08702 (p) 13814
(q) 2·456 (r) 45192 (s) 29·302 (t) 0·756
3. Calculate and give your answer correct to 2 significant figures
(a) 5·16 22·7 (b) 27·3 6·84 (c) 3·14 92
(d) 25·8 1·76 1·1 (e) 13·2 3·72 (f) 25·8 52·9
(g) 1·142 2·92 (h) 5·2 0·.49 30·3 (i) 234 (0·028 33)
(j) (0·08 252) 3 (k) (1·05)
2 455 (l) 3·14 12
2 7
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Calculate distance given speed and time
1. Calculate the distance, in kilometres, covered by a car travelling at
(a) 50 km /h for 3 hrs (b) 40 km/h for 4 hrs (c) 60 km/h for 2 hrs
(d) 45 km /h for 2 hrs (e) 80 km/h for 3 hrs (f) 75 km/h for 5 hrs
(g) 64 km /h for 6 hrs (h) 52 km/h for 4 hrs (i) 96 km/h for 3 hrs
(j) 48 km /h for 4 hrs (k) 24 km/h for 7 hrs (l) 110 km/h for 2 hrs
2. Calculate the distance, in miles, covered by a car travelling at
(a) 50 mph for 2 ½ hrs (b) 36 mph for 1 ½ hrs (c) 64 mph for 3 ½ hrs
(d) 60 mph for 3·5 hrs (e) 70 mph for 1·5 hrs (f) 42 mph for 2·5 hrs
(g) 62 mph for 4 ½ hrs (h) 38 mph for 2 ½ hrs (i) 54 mph for 1 ½ hrs
(j) 70 mph for 2·4 hrs (k) 48 mph for 3·5 hrs (l) 60 mph for 4·2 hrs
3. Calculate the distance travelled for each journey below. Remember the working and the
units !
How far have you gone if you travel for .....
(a) 4 hours at a speed of 50 km/h?
(b) 6 hours at a speed of 65 mph?
(c) 2 2
1 hours at a speed of 87 km/h?
(d) 40 minutes at a speed of 300 metres per minute? (answer in kilometres)
(e) 30 minutes at a speed of 48 mph?
4. A plane flies at a maximum speed of 460 km/h.
(a) How far will it travel in 7 hours at maximum speed ?
(b) The pilot wants to fly to Rio, a distance of 5900 km.
Can he complete the journey within 13 hours? Explain your answer.
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5. A luxury cruiser has a maximum speed of 28 km/h.
(a) How far can the boat sail in 3 4
1 hours at top speed?
(b) On a journey from one island to another the cruiser has to navigate
between two reefs, breaking the crossing into three stages.
Stage 1 : 2 hours at half-speed.
Stage 2 : 4 2
1 hours at full speed.
Stage 3 : 3 hours at one-quarter speed.
Calculate the total distance travelled on the journey.
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EXTENSION – finding Speed and Time
Time
DistanceSpeed
1. Calculate the speed, in km/h, of a car travelling :
(a) 480 km in 8 hrs (b) 350 km in 7 hrs (c) 240 km in 3 hrs
(d) 260 km in 4 hrs (e) 500 km in 5 hrs (f) 432 km in 6 hrs
(g) 92km in 2 hrs (h) 228 km in 3 hrs (i) 224 km in 4 hrs
(j) 195 km in 3 hrs (k) 332 km in 4 hrs (l) 357 km in 7 hrs
2. Calculate the speed, in mph, of a car travelling:
(a) 125 mls in 2 ½ hrs (b) 96 mls in 1 ½ hrs (c) 287 mls in 3 ½ hrs
(d) 114 mls in 1 ½ hrs (e) 288 mls in 4 ½ hrs (f) 165 mls in 2 ½ hrs
(g) 306 mls in 4·5 hrs (h) 135 mls in 2·5 hrs (i) 57 mls in 1·5 hrs
(j) 210 mls in 3·5 hrs (k) 264 mls in 5·5 hrs (l) 105 mls in 2·5 hrs
Speed
DistanceTime
3. Calculate the time taken, in hours, by a car travelling:
(a) 480 km at 80 km/h (b) 720 km at 60 km/h (c) 640 km at 64 km/h
(d) 405 km at 45 km/h (e) 285 km at 95 km/h (f) 315 km at 63 km/h
(g) 152 km at 76 km/h (h) 564 km at 94 km/h (i) 462 km at 66 km/h
(j) 294 km at 98 km/h (k) 553 km at 79 km/h (l) 344 km at 86 km/h
4. Calculate the time taken, in hours, by a car travelling
(a) 480 mls at 60 mph (b) 350 mls at 70 mph (c) 400 mls at 40 mph
(d) 440 mls at 55 mph (e) 282 mls at 47 mph (f) 273 mls at 39 mph
(g) 160 mls at 64 mph (h) 175 mls at 50 mph (i) 99 mls at 66 mph
(j) 144 mls at 60 mph (k) 320 mls at 50 mph (l) 319 mls at 58 mph
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Time Intervals (12 hour time)
1. Calculate the number of hours between:
(a) 3 a.m. and 7 a.m. (b) 2 p.m. and 8 p.m (c) 8 a.m. and 11 a.m.
(d) 2 a.m. and 10 a.m. (e) 1 p.m. and 11 p.m (f) 9 a.m. and 10 a.m.
(g) 9 a.m. and 1 p.m. (h) 7 a.m. and 3 p.m (i) 5 a.m. and 2 p.m.
(j) 10 a.m. and 6 p.m. (k) 8 a.m. and 8 p.m (l) 11 a.m. and 7 p.m.
2. Calculate the number of hours and minutes between:
(a) 2 a.m. and 5.30 a.m. (b) 7.15 p.m. and 9.30 p.m
(c) 12.30 p.m. and 4 p.m. (d) 2.15 a.m. and 3.45 a.m.
(e) 8.30 p.m. and 10.45 p.m (f) 10 a.m. and 12.45 p.m.
(g) 7.30 a.m. and 9.15 a.m. (h) 1.30 p.m. and 8.15 p.m
(i) 10.30 a.m. and 4.45 p.m. (j) 5 a.m. and 2.15 p.m.
(k) 7.30 a.m. and 6.15 p.m (l) 11.15 a.m. and 12.45 p.m.
3. Calculate the number of hours and minutes between:
(a) 10 p.m. and 3 a.m. (b) 7 p.m. and 9 a.m (c) 8 p.m. and 11 a.m.
(d) 2 p.m. and 10 a.m. (e) 11 p.m. and 8 a.m (f) 9 p.m. and 2 a.m.
(g) 10.30 p.m. and 1.30 a.m. (h) 7.30 p.m. and 2.45 a.m
(i) 9.30 p.m. and 12.30 a.m. (j) 10.15 p.m. and 6.30 a.m.
(k) 8.45 p.m. and 9 a.m (l) 10.30 p.m. and 2.15 p.m.
4. Jamie leaves his house at 8.15 a.m and arrives at school at 8.45 a.m. How long does it
take him to travel to school?
5. Kathleen is a nurse. She begins her shift at 10.15 p.m and
finishes at 6.45 a.m.
How many hours and minutes does she work?
6. Shakeela is a salesperson. She leaves home at 11.45 a.m. to keep an appointment
at 1.15 p.m.
How long does she have to make her journey?
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7. The overnight bus to London leaves Glasgow at
10.15 p.m. and arrives in London at 7 a.m.
How long does the journey take?
8. The Beepee garage shop is open from 6.30 a. m. to 10.15 p.m.
How long is it open for, in hours and minutes?
9. What time will it be?
(a) 16 minutes after 1.36 p.m. (b) 35 minutes after 2.34 p.m.
(c) 12 minutes after 4.25 a.m. (d) 10 minutes after 5.40 a.m.
(e) 24 minutes after 11.36 p.m. (f) 38 minutes after 6.45 a.m.
What time was it? …….
10. (a) 10 minutes before 3.15 p.m. (b) 25 minutes before 8.20 p.m.
(c) 20 minutes before 5.45 a.m. (d) 50 minutes before 4.05 a.m.
(e) 14 minutes before 2.30 p.m. (f) 38 minutes before 2.15 a.m.
11. (a) 1 hour after 2.30 p.m. (b) 2 hour after 9.15 a.m.
(c) 4 hours after 3.15 p.m. (d) 3 hours after 5 a.m.
(e) 16 hours after 5.29 p.m. (f) 12 hours after 6 p.m.
12. (a) 2 hours before 11.45 a.m. (b) 6 hours before 12.35 p.m.
(c) 9 hours before 7.45 a.m. (d) 12 hours before 2.40 p.m.
(e) 5 hours before 4.30 a.m. (f) 7 hours before 5.30 p.m.
13. (a) 1 hour 30 mins after 2.30 p.m. (b) 2 hours 15 mins after 3.45 a.m.
(c) 2 hours 20 mins after 8.45 p.m. (d) 5 hours 10 mins after 4.56 p.m.
(e) 6 hours 45 mins after 10.35 a.m. (f) 2 hours 30 mins after 11.50 p.m.
14. (a) 2 hours 15 mins before 4.30 p.m. (b) 6 hours 10 mins before 6.45 a.m.
(c) 4 hours 30 mins before 4.15 a.m. (d) 7 hours 53 minutes before 9.45 p.m.
(e) 13 hours 30 mins before 8.15 p.m. (f) 21 hours 12 minutes before 11.30 p.m.
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15. Mandy has an appointment with the hairdresser in Glasgow at 2.30 pm. She wants to
arrive 15 minutes before that.
(a) When will she arrive at the hairdresser?
(b) It takes 40 mins to get into town on the train and 10 minutes
from her house to the station. When should she leave home to
get a train which leaves at 1 pm?
(c) Her journey home will take 55 minutes altogether and she must
be home by 5 pm.
When is the latest time she could leave Glasgow to go home?
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Time Intervals (24 hour time)
1. Calculate the number of minutes between:
(a) 2305 and 2340 (b) 1530 and 1555 (c) 1543 and1603
(d) 1432 and 1456 (e) 1749 and 1823 (d) 2235 and 2307
2. Calculate the number of hours between:
(a) 0100 and 1300 (b) 1235 and 1635 (c) 0915 and 2115
(d) 0350 and 2150 (e) 0730 and 2230 (d) 1035 and 2335
3. Calculate the number of hours and minutes between:
(a) 1215 and 1425 (b) 0450 and 0710 (c) 1845 and 2030
(d) 0755 and 2315 (e) 0315 and 1835 (f) 1235 and 1510
4. What time will it be?
(a) 12 minutes after 0936 (b) 50 minutes after 1306
(c) 35 minutes after 1635 (d) 15 minutes after 1750
(e) 53 minutes after 1130 (f) 18 minutes after 1843
5. What time was it?
(a) 15 minutes before 1325 (b) 40 minutes before 1250
(c) 35 minutes before 1550 (d) 46 minutes before 2336
(e) 55 minutes before 2120 (f) 23 minutes before 1208
6. What time will it be?
(a) 2 hours after 2100 (b) 3 hours after 1408
(c) 9 hours after 2115 (d) 12 hours after 1523
(e) 5 hours after 0231 (f) 18 hours after 0435
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7. What time was it?
(a) 3 hours before 2300 (b) 4 hours before 1634
(c) 11 hours before 2109 (d) 13 hours before 1130
(e) 15 hours before 1750 (f) 23 hours before 2106
8. What time will it be?
(a) 3 hours 15 minutes after 0445 (b) 8 hours 50 mins after 0545
(c) 12 hours 10 minutes after 1055 (d) 4 hours 55 minutes after 1352
(e) 6 hours 55 minutes after 1243 (f) 2 hours 34 minutes after 1448
9. What time will it be?
(a) 1 hour 20 mins before 1240 (b) 3 hours 45 mins before 1550
(c) 6 hours 20 mins before 1800 (d) 2 hours 17 mins before 1214
(e) 5 hours 55 mins before 2345 (f) 13 hours 23 minus before 1502
10. Kevin wants to catch a bus that leaves at 1130. If it takes 10 mins to walk to the bus stop,
when should he leave the house?
11. Barry has to travel to work by bus. It takes him 5 minutes to walk to the bus stop and 30
minutes to get to work. He likes to arrive at work 15 minutes early.
When should he leave his house in order to get to work
for starting at 8 am?
12. (a) A film on TV starts at 1930 and lasts for 2 hours 45 minutes?
When will it end?
(b) Kelly wants to watch a programme which lasts for 1 hour 20 minutes and
finishes at 1845. She doesn’t get home from work until 1730.
Will she be on time to see the start of the programme?
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TIMETABLES(1)
Alison attends Anywhere High School. Here is her timetable. School starts at 900 am.
Answer these questions from the timetable above:
1. (a) How many Maths lessons does Alison have each week?
(b) Is this the same as you?
2. Alison has an appointment with her Guidance Teacher at 10.15 on Wednesday. Which
subject is she going to miss?
3. At 12.30 on Friday she has a Violin lesson. Which period was this?
4. Which subject is Alison in on Wednesday at 2.45 pm?
5. Alison was not feeling well one day and had to go home at the end of lunchtime.
At what time did she leave to go home?
6. On Monday her bus was late and she arrived in school at 10.30 a.m.. Which subject did
she have to go to after she had signed in?
R 1 2 3 4 5 6
E 9.10-
10.05
10.05-
11.00
11.15-
12.05
12.05-
12.55
1.40-2.35 2 .35-3.30
Monday G MATHS ENGLISH B FRENCH HISTORY L CRAFT MUSIC
Tuesday PE MATHS R DRAMA IT U ENGLISH HE
Wednesday FRENCH ART E PSD RE N MATHS ENGLISH
Thursday ENGLISH HISTORY A ART IT C SCIENCE CRAFT
Friday FRENCH SCIENCE K MATHS PE H MUSIC DRAMA
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7. How many minutes does the interval last?
8. How long is lunchtime?
9. (a) 15 minutes into lunchtime, Alison goes to Band practise. At what time is this?
(b) The practise finishes 5 minutes before the end of lunchtime. How many
minutes does it last?
10. Alison arrives at school 15 minutes before registration starts. When does she get to
school?
11. The school bus leaves 10 minutes after the end of period 6. At what time does it leave?
12. (a) How many minutes does Alison spend in registration each day?
(b) How many minutes is this for the whole week?
13. (a) How many minutes of PE does Alison have each week?
(b) How many hours and minutes is this?
14. (a) How many minutes of English does she have each week?
(b) How many hours and minutes is this?
15. Copy this table into your jotter and fill in the blanks to show how many minutes each
period lasts.
Period 1 Period 2 Period 3 Period 4 Period 5 Period 6
55 minutes 50 minutes
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16. How many hours and minutes is it from the beginning of Period 5 until the end of the
school day?
17. How many minutes is Alison in class during Periods 1, 2, 3 and 4 altogether?
18. How many hours and minutes is it from the beginning of the day at 9.00 am until
the end of the day at 3.30 pm?
19. How many hours and minutes are spent in school each week including intervals and
lunchtimes?
20. (a) How many hours and minutes do the intervals take up each week?
(b) How many hours and minutes do the lunchtimes take up each week?
(c) How many hours and minutes are spent in class each week?
21. (a) Alison leaves home at 8.15 in the morning and arrives home at 4.20 in the
afternoon.
How many hours and minutes is she away from home altogether each day?
(b) How many hours and minutes is this each week?
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TIMETABLES(2)
Here is a list of the TV programmes on BBC 1 and ITV 1 one Sunday.
BBC 1 ITV 1
12.00 Politics 12.00 Eye to Eye
1.00 Eastenders 12.30 Seven Days
2.25 Sportscene 1.00 News
5.10 News 1.55 Scotland Today
5.35 Songs of Praise 2.00 Driving Miss Daisy
6.15 Last of the Summer Wine 3.55 That’s Esther
6.45 Antiques Roadshow 4.25 Scotsport
7.30 Holiday Swaps 6.10 Gaelic Programme
Answer these questions from the information given above:
1. Copy and fill in this table to show which programme is on at the times given.
TIME BBC 1 ITV 1
1.00
12.00
6.15
5.45
2.30
2. Gordon finished his homework at 2.45.
(a) What programme could he watch on BBC 1 at that time?
(b) How many minutes had the film on ITV 1 been on at that time?
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3. Sally wanted to see Songs of Praise but didn’t switch on until 15 minutes
after it had started.
(a) When did she switch on?
(b) What was on ITV 1 at the same time?
4. Holly wanted to watch Driving Miss Daisy and switched on 20 minutes early.
(a) What was on ITV 1 then?
(b) What was on BBC 1?
5. Peter watched Seven Days on ITV and then switched over to BBC 1.
(a) Which programme was coming on then?
(b) What was on ITV by the time this programme ended?
6. (a) For how many minutes did the News on BBC 1 last?
(b) What about the news on ITV 1?
(c) How many minutes of news altogether?
(d) How many hours and minutes is this?
7. (a) How many minutes did Antiques Roadshow last?
(b) How many minutes did Last of the Summer Wine last?
(c) How long is this altogether? [Answer in hours and minutes].
8. Stewart watched Eye to Eye on ITV 1 and then planned to watch Eastenders on BBC 1.
(a) How long would he have to wait between programmes?
(b) What else could he watch on ITV 1 to pass the time?
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9. David wanted to watch Eastenders and then the film, Driving Miss Daisy. How many
minutes of the film did he miss?
10. Jenny was going out so decided to tape her favourite programmes.
She set up her video to record: Driving Miss Daisy, Songs of Praise and The Antiques
Roadshow,
(a) Write down how long each programme lasted.
(b) How long did the three programmes last altogether?
11. (a) How many hours and minutes did Scotsport last?
(b) How many hours and minutes did Sportscene last?
(c) Which was the longer sports programme?
(d) How many hours and minutes of sport were on altogether?
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TIMETABLES (3)
The School Outdoor Club were going away for a weekend. Here is the programme of activities
for Saturday.
600 am 5 mile run to waken up!
800 BREAKFAST
830 Planning the route for a midnight hike
900 Abseiling
1100 BREAK
1130 Canoeing
115 LUNCH
215 Learn Mountaineering Skills
300 Leisure Swimming
500 An introduction to Bungee Jumping
700 DINNER
930 Set off for Midnight Hike
130 am Return from hike and go to bed.
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Answer the following questions from the details given in the programme sheet:
1. How long did they spend: (a) Planning the Midnight Hike
(b) Swimming
(c) Learning Mountaineering skills
(d) Canoeing
(e) On the midnight hike?
2. How long did the morning break last?
3. How long did they get for lunch and dinner altogether?
4. All the members had to arrive at the canoeing 15 minutes before the time given.
(a) When did they have to arrive?
(b) If they left 20 minutes after it ended, when did they leave?
(c) How much of lunch time was left?
5. Malcolm arrived at 10.45 and joined in the activity at that time.
(a) What activity did he join?
(b) How many minutes late was he?
(c) How long was left of this activity?
(d) What activities had he missed?
6. The instructor for the Bungee Jumping arrived 30 minutes after the starting time.
(a) At what time did he arrive?
(b) How long was left?
(c) If he stayed for the full 2 hours, when did the Bungee Jumping Session end?
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7. Joseph, Keiron and Daniel decided to have a competition to see who could complete the
hike in the shortest time.
They all set out together at 9.30 but came back at different times. Here is a list of when
they arrived back.
Joseph: 12.45 am
Kieron: 15 minutes before Joseph
Daniel: 30 minutes after Joseph.
Copy and complete this table:
(a) Who arrived back first?
(b) Who was last?
(c) How many minutes after the winner?
NAME LEAVING
TIME
ARRIVING
BACK TIME
TOTAL TIME
TAKEN
Joseph 9.30 12.45
Kieron 9.30
Daniel 9.30
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Ratio(1)
1. (a) Divide £50 in the ratio 7:3 . (b) Divide 80kg in the ratio 7:3 .
(c) Divide £35 in the ratio 2:5 . (d) Divide 240 g in the ratio 1:4 .
2. (a) Three boys, Harry, James and Bill divide £120 in the ratio 8:3:1
How much does each boy get?
(b) Three girls, Susan, Beth and Jill divide £56 in the ratio 7:5:2 .
How much does each girl get?
3. Graeme and Fred invest £3400 in a new company.
(a) If the money each of them put in was in the ratio 3 : 7 , how much did Fred invest
in the new company?
(b) They decide to split the profits in the same ratio as their investment.
If they made £6200 profit, how much of the profit will Graeme get?
4. The ratio of boys : girls in a class is 4 : 5. If there are 27 pupils in the class, how many
girls are there?
5. (a) In a piece of jewellery the ratio of gold to silver is 5 : 2.
If the jewellery contains 56g of gold, what weight of silver does it contain?
(b) An lottery win was shared between three brothers, Dave, Frank and Pat, in the ratio
1 : 3 : 4.
If Pat received £824, how much did each of the other two brothers receive?
6. Two farmers, Bill and Dan, decided to split a herd of cows in the ratio 5 : 7.
(a) If Dan's share was 42 cows, how many cows did Bill get ?
(b) How many cows were there altogether ?
(c) A third farmer, George, came along and the three farmers decided to split the herd
in the ratio (B : D : G) 3 : 4 : 1.
How many cows will each farmer get?
£
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Ratio(2)
1. (a) Divide £48 in the ratio 5:3 . (b) Divide £100 in the ratio 3:7 .
(c) Divide £56 in the ratio 6:1 . (d) Divide £50 in the ratio 1:4 .
(e) Divide £120 in the ratio 3:5 . (f) Divide £75 in the ratio 7:8 .
(g) Divide £36 in the ratio 5:4 . (h) Divide £240 in the ratio 7:5 .
2. (a) Three boys divide £88 in the ratio 7:3:1 . How much does each boy get?
(b) Three girls divide £48 in the ratio 11:3:2 . How much does each girl get?
(c) Three men divide £60 in the ratio 5:4:3 . How much does each man get?
(d) Three girls divide £96 in the ratio 5:2:1 . How much does each girl get?
3. John and David inherit £3400. If they divide the money in the ratio 2 : 3, how much
does each person receive?
4. The ratio of boys : girls in a class is 3 : 5. If there are 32 pupils in the class, how many
girls are there?
5. The ratio of sand : cement in a certain concrete is 7 : 4. If a cement mixer has been filled
with 33 bags, how many of the bags were sand?
6. (a) The ratio of cats : dogs in an animal hospital is 1 : 5.
If there are 8 cats, how many dogs are there?
(b) In a school show the ratio of girls : boys is 2 : 1.
If there are 24 girls, how many boys are there?
(c) In a necklace the ratio of diamonds : emeralds is 3 : 4.
If there are 16 emeralds, how many diamonds are there?
(d) An estate was shared between three brothers, Tom, John and Dave, in the
ratio 2 : 3 : 5.
If Tom received £2400, how much did each of the other two brothers receive?
Pegasys 2013
7. Three friends, Xena,Gabrielle and Joxar, have found a treasure chest full of gold coins.
They decide to split the coins in the ratio 5 : 3 : 1.
(a) If Gabrielle was to receive 24 coins, how many coins would the others get?
(b) How many coins are there altogether?
(c) Before they can share out the coins, Calisto arrives, and persuades
the friends to split the coins in the ratio (X : G : J : C) 9 : 5 : 4 : 6 .
How many coins will each person now receive?
Pegasys 2013
Volume of Cube and Cuboid
1. Calculate the volume of a cube with
(a) l = 3cm (b) l = 7cm
(c) l = 2cm (d) l = 4cm
(e) l = 5cm (f) l = 10cm
(g) l = 6cm (h) l = 9cm
(i) l = 8cm (j) l = 14cm
(k) l = 11cm (l) l = 20cm
Volume of a cube , V = l3
2. Calculate the volume of a cuboid with
(a) l = 5cm, b = 4cm, h = 3cm
(b) l = 7cm, b = 3cm, h = 2cm
(c) l = 10cm, b = 8cm, h = 3·5cm
(d) l = 4cm, b = 4cm, h = 3cm
(e) l = 20mm, b = 8mm, h = 10mm
(f) l = 5·5cm, b = 1·4cm, h = 7cm
(g) l = 0·2m, b = 1m, h = 1·8m
Volume of a cuboid , V = lbh (h) l = 4·5cm, b = 2·5cm, h = 4cm
(i) l = 2cm, b = 4cm, h = 1m
(j) l = 15cm, b = 80mm, h = 5cm
l
l b
h
Pegasys 2013
3. Find the volume of a rectangular-based prism for the values of l, b and h given.
(a) l = 6cm b = 4cm h = 5cm
(b) l = 8cm b = 3cm h = 6cm
(c) l = 3m b = 1m h = 2m
(d) l = 18cm b = 12cm h = 10cm
(e) l = 7cm b = 7cm h = 7cm
(f) l = 7·5cm b = 4cm h = 12cm
(g) l = 8·3cm b = 2·7cm h = 10cm
(h) l = 12·8cm b = 6·5cm h = 4·3cm
(i) l = 150mm b = 40mm h = 85mm
(j) l = 14·5cm b = 14·5cm h = 34cm
4. Find the volume of a concrete block measuring
36cm by 18cm by 12cm.
5. A classroom measures 9m by 7m by 3m.
How many pupils can it hold if each pupil need 6m3
of air space?
6. (a) Find the volume of a swimming pool which
measures 1500cm by 1000cm by 200cm.
(b) If 1litre = 1000cm3, calculate the number of litres of
water that the pool will hold.
l
b
h
Pegasys 2013
Finding the area of a shape
Find the area of each of the shapes shown below.
1. 2. 3.
4. 5.
6. 7.
8. 9.
2cm
3cm
4cm
2cm
4cm
4cm
2cm
1cm
7cm
5cm
4cm
10cm
3cm
6cm
9cm
6cm
12cm
20cm
7cm
8cm 5cm
15cm
8cm
7cm
7cm 7cm
8cm
30cm
25cm
14cm
9cm
9cm
12cm
14cm
40cm
1·8cm
9cm
7·2 cm 5·2 cm 6·4 cm 2cm 2cm 2cm 2cm 2cm
2cm
8cm
Pegasys 2013
Find the perimeter of a shape
1. Find the perimeter of each of the shapes shown below.
(a) (b) (c)
(d) (e)
(f) (g)
(h) (i)
2cm
3cm
4cm
2cm
4cm
4cm
2cm
1cm
7cm
5cm
4cm
10cm
3cm
6cm
9cm
6cm
12cm
20cm
7cm
8cm 5cm
15cm
8cm
7cm
7cm 7cm
8cm
30cm
25cm
14cm
9cm
9cm
12cm
14cm
40cm
1·8cm
9cm
7·2 cm 5·2 cm 6·4 cm 2cm 2cm 2cm 2cm 2cm
2cm
8cm
Pegasys 2013
2. Find the perimeter of each of the shapes shown below.
(a) (b) (c)
(d) (e)
27cm
15m
18m
40m 20m 20m
13cm
14cm
80cm
25cm
70cm 50cm
24cm
24cm
19·8cm
89cm
35·4cm
2·4m
3·8m
25m
8·4cm 17·2cm
35·2cm 35·2cm
Pegasys 2013
Calculate rate
1. Find the cost of one of each item in the examples below.
(a) 7 books cost £31.43 (b) 5 calculators cost £17.50
(c) 4 bars of chocolate cost £1.28 (d) 9 T-shirts cost £81
(e) 12 eggs cost £1.80 (f) 3 metres of cloth cost £25.50
(g) 6 bottles of cola cost £5.34 (h) 8 pens cost £1.52
2. (a) A train travels 325miles in 5 hours. How far does it travel in 1 hour?
(b) A car travels 144km on 6 litres of petrol. How far will it go on 1 litre?
(c) A factory makes 36400 cars per year. How many does it make in 1 week?
(d) A typist can type 840 words in 1 hour. How many can she type in 1 minute?
(e) A family uses 21 pints of milk in a week. How many do they use a day?
(f) 10 apples weigh 2kg. What does one apple weigh?
(g) A man earns £28.80 for an 8-hour day. What does he earn in an hour?
(h) A car travels 72km in an hour. How far does it travel in 1 minute?
3. (a) 3 kg of carrots cost £1.44. 5kg of carrots cost £2.30. Which pack is the best value?
(b) One car travels 110 miles in 2 hours and another travels 270 miles in 5 hours.
Which car is the faster?
(c) John earns £278.61 for working 37 hours. Jim earns £339.30 for working 45 hours.
Who earns the higher rate per hour?
(d) Paula can type 3300 words in 4 hours. Christeen one can type 2469 words in 3
hours. Who types more words per hour?
(e) 5 chocolates éclairs cost £4.25. 3 meringues cost £2.70. Which cake is the cheaper?
(f) 6 teddies cost £108. 7 dolls cost £125.30. Which one is the cheaper?
(g) In a factory, machine A can produce3600 packets of sweets in 3 hours and machine
B produces 7875 packets in 7 hours. Which machine works the faster?
Pegasys 2013
Best Buy
Which item is the best buy in each group below?
(a) (b)
(c) (d)
(e) (f)
(g) (h)
(i) (j)
6 kg
£10.50
2·5kg
£4.80 1·5kg
£3.06
Twin pack
(2 × 3·5kg)
£11.90
250ml
80p
650ml
£1.99
3 litres
£1.68 2 litres
£1.20
1 litre
£0.62
550 g
£8.20
3 litres
£1.74 1·5 litres
84p
0 8 litres
48p
350 g
£5.60
200 g
£3.60
1 kg
£1.80
750 g
£1.20
500 g
£1.00
200 g
44p
4 litres
£2.56 2 litres
£1.39
150ml
£1.20
0 7 litre
40p 250ml
£1.75
500ml
£2.50
0·8kg
£4.20
0·5kg
£2.80 0·3kg
£1.59 600 g
£2.50
320 g
£1.40
200 g
£1.05
550ml
£1.60 950ml
£2.95
Pegasys 2013
Direct Proportion
1. (a) One ream of paper contains 500 sheets. How many sheets in 4 reams?
(b) Car parking charges are 30p per hour. What is the cost for 3 hours?
(c) 1 cm3 of lead weighs 11·3 g. What is the weight of 6cm
3?
(d) A packet of sweets contains 182 kcal. How many kcal in 5 packets of sweets?
(e) On a plan 1 cm represents 12 metres. How many metres does 7 cm represent?
(f) One bottle contains 350 ml. How much will 12 bottles contain?
(g) One ice-cream cone costs 80p. What will 5 cost?
(h) £1 can be exchanged for 1.14Euros. How many francs will you get for £10?
2. (a) A machine a factory fills 840 bottles in 6 hours. How many bottles will it fill in
5 hours?
(b) Eggs cost £1.80 per dozen. What would 15 eggs cost?
(c) 90 nails weigh 2 kg. What will 315 nails weigh?
(d) A car can travel 176 km on 8 litres of petrol. How far can it travel on 5 litres ?
(e) The width of 6 identical textbooks is 11.4 cm. What is the width of 9 of the same
books?
(f) Daniel earns £143.50 for working a 35 hour week. How much will Stefan earn
for a 40-hour week paid at the same rate?
(g) A hiker walked steadily for 4 hours and covered a distance of 16 km.
How long did he take to cover 12 km?
(h) It cost £218 to turf a lawn of area 64 m2. How much would it cost to turf a lawn of
area 56 m2?
(i) It costs £588 to hire scaffolding for 42 days. How much would it cost to hire the
same scaffolding for 36 days at the same rate per day?
(j) A typist typed 3960 words in 4 ½ hours. How long would it take to type 2860
words at the same rate?
(k) A typist charges £37.50 for work which took her 6 hours.How much would she
charge for 9 hours work at the same rate ?
Pegasys 2013
3. A rail journey of 300 miles costs £72. At the same rate per mile,
(a) What would be the cost of travelling 250 miles?
(b) How far could you travel for £42?
4. At a steady speed, a car uses 15 litres of petrol to travel 164 km.
At the same speed, what distance could be travelled if 6 litres of petrol were used?
5. A scale model of a ship is designed so that the mast is 9 cm
high and the mast of the original ship is 12 m high.
The length of the original ship is 27 m.What is the length of
the model ship?
6. A ream of paper (500 sheets) is 6·2 cm thick. How thick is a pile of 350 sheets of the
same paper?
7. 24 identical mathematics books will take up 60 cm of shelf space.
How many books will fit into 85 cm?
8. A D.I.Y. enthusiast makes a small coffee table. Below is a list of the cost of materials and
the actual amount of materials that he needs.
Materials Costs
4 legs each 40 cm long 2 m costs £3.20
4 stretchers each 80 cm long 3 m costs £2.10
1 top 1·5 square metres 1 square metre costs £1.50
0·75 litre of varnish 1 litre costs £4.80
12 screws 20 screw cost 80p
What is the total cost of the materials that are actually used?
Pegasys 2013
Direct Proportion again
1. 300g of flour is used to make 6 cakes. How much flour is needed to make:
(a) 12 such cakes? (b) 3 cakes? (c) 9 cakes?
2. Eight bars of chocolate cost £3.36. Calculate the cost of:
(a) 1 bar of chocolate (b) 3 bars (c) 11 bars.
3. A stack of six identical books weighs 381 kg. How much would a stack of 10 books
weigh?
4. (a) 4 cakes cost £3.12. Find the cost of 9 cakes.
(b) The height of 12 stacked CD cases is 8136 mm. Calculate the height of 7 such
cases.
(c) A row of 24 staples measures 144 mm. How long would a row of 38 staples be?
(d) The weight of 3 baskets of fruit is 45 kg. Calculate the weight of 5 baskets.
5. Carpet is priced relative to its area.
A rectangular carpet measuring 5m by 4m costs £264.
(a) Calculate the cost for 1 square metre of this carpet. (the cost per sq.m)
(b) How much would a carpet measuring 8m by 6m cost?
6. A bedroom carpet measuring 4m by 7m costs £180.60.
How much would the same type of carpet measuring 5m by 8m cost?
7. A car uses 15 litres of petrol to travel 210 miles. How much petrol would the car use for a
journey of 378 miles at the same rate of consumption?
8. Fifteen books cost £123. How many books could you buy for £73.80?
9. For £250 you receive 2750 francs. How much would 1364 francs cost you in pounds
sterling?
14
Pegasys 2013
Hire Purchase
1. For each of the items below, calculate (i) the total hire purchase cost
(ii) the extra over the cash price
2. A mail order company sells a sofa for £469.95. It offers 3 alternative ways to pay
(i) deposit of £69.95 and 24 monthly payments of £20.50
(ii) deposit of £49.95 and 18 monthly payments of £26.90
(iii) deposit of £39.95 and 12 monthly payments of £39.20
Which is (a) the cheapest way to buy the sofa?
(b) the dearest way to buy the sofa?
3. The Osnam family have had new windows installed. They had the choice of paying for
them in two different ways.
Option 1: 36 monthly payments of £134.75.
Option 2: a deposit of £1971 then the remainder in equal
monthly payments over 2 years.
Both options cost the same in total and they chose Option 2.
Calculate the amount of each payment.
Item Cash Price Hire Purchase Terms
Deposit Payments
(a) Television Set £330 £33 12 months @ £28
(b) Microwave Oven £118 £15 6 months @ £20
(c) Music System £279 £35 18 months @ £15
(d) Fridge/Freezer £390 £40 12 months @ £32
(e) Bedroom Furniture £510 £50 24 months @ £21.50
(f) Video Camera £449 £45 12 months @£35.75
(g) Golf Clubs £283 £28 9 months @ £33
(h) Dining Table & Chairs £499 £50 18 months @ £27.80
Pegasys 2013
4. For each of the items below, calculate i. the deposit
ii. the total hire purchase cost
iii. the extra over the cash price
5. A car costing £7200 can be paid for in three ways.
(i) by cash
(ii) by hire purchase with a deposit of £2000 and 24 monthly payments of £260
(iii) by hire purchase with a deposit of 25% and 36 monthly payments of £186
Calculate the difference between the most and least expensive methods.
6. An Internet TV can be bought for a cash price of £2400.
It can be paid for by making a deposit of 5
2 of the cash price followed by 12 equal
monthly payments.
Calculate the cost of each payment.
Item Cash Price Hire Purchase Terms
Deposit Payments
(a) Oven £450 10% 12 months @ £38
(b) Computer £780 10% 18 months @ £44
(c) Bicycle £195 20% 6 months @ £33.50
(d) Diamond Ring £370 15% 12 months @ £31.20
(e) Carpet £410 20% 24 months @ £17.40
(f) 3 piece suite £920 15% 36 months @£26.10
(g) Car £3285 25% 48 months @ £69.50
(h) Fax Machine £229 10% 9 months @ £25.70
Pegasys 2013
Holiday Money (1)
The following questions use this table of exchange rates, which gives the amount of each
currency you will receive in exchange for £1.
1. Change each of the following amounts into USA dollars:
(a) £5 (b) £31 (c) £462 (d) £20
(e) £44 (f) £9 (g) £207 (h) £36
(i) £65 (j) £4.50 (k) £85.50 (l) £17.50
2. Change each of the following amounts into (i) Euros
(ii) Yen :
(a) £4 (b) £49 (c) £185 (d) £30
(e) £27 (f) £7 (g) £304 (h) £52
(i) £83 (j) £10 (k) £0.50 (l) £18.50
3. Change each of the following amounts into Australian dollars:
(a) £6 (b) £57 (c) £19 (d) £206
(e) £135 (f) £23 (g) £2 (h) £77
(i) £34 (j) £480 (k) £0.50 (l) £29.50
4. Maria and Vicki are going on a school trip to Europe. Maria has saved £110 spending
money and Vicki has saved £94. How much will they each get when they change their
money into Euros?
Country Currency Rate per £
USA Dollars ($) $1.55
JAPAN Yen (¥) 150 ¥
EUROZONE Euros(€) 1.16 €
AUSTRALIA Dollars ($) 1.7 $
Pegasys 2013
5. Martin is travelling to America on a business trip. He changes £550 into dollars before
he goes.
(a) How many dollars does he receive?
(b) If he spends $800 how any dollars will he have left?
6. Carol is going on holiday to Japan with her parents. She takes £75 of her savings to the
bank to change into yen.
(a) How many yen does she receive?
(b) At the end of her holiday she has 1420 yen left. How many yen did she spend?
Holiday Money (2)
The following questions use this table of exchange rates which gives the amount of each currency
you will receive in exchange for £1.
1. Change the following amounts into pounds:
(a) 600 k (b) 1920 k (c) 4440 k (d) 5640 k
(e) 7680 k (f) 123600 k (g) 25680 k (h) 160800 k
(i) 5424 k (j) 7572 k (k) 131316 k (l) 870 k
2. Change the following into pounds:
(a) $ 48 (b) $84 (c) $432 (d) $156
(e) $ 1200 (f) $2040 (g) $4200 (h) $22800
(i) $ 3936 (j) $1800 (k) $12 (l) $237.6
Country Currency Rate per £
ICELAND Kroner (k) 120 k
SWITZERLAND Francs (f) 1.43 f
INDIA Rupees (r) 94.55 r
CANADA Dollars ($) $160
SOUTH AFRICA Rand (R) 152 R
Pegasys 2013
3. Change the following sums of money into pounds [Answer to nearest penny]:
(a) 490 r (b) 245 r (c) 58800 r (d) 36750 r
(e) 25480 r (f) 8820 r (g) 3430 r (h) 98000 r
(i) 2352 r (j) 933 r (k) 6076 r (l) 441 r
4. Jean-Pierre is visiting some friends in England. He bought some presents in Geneva
before he left home. The presents are shown below. How much did each item cost in
pounds?
5. Riz has been on holiday in India. He comes home with 945 rupees. How much is this in
pounds ?
6. Soraya changes £245 into Rand for a visit to South Africa.
(a) How many Rand does she receive?
(b) She spends 3344 Rand. How much does she have left?
(c) When she returns she exchanges her Rand. How many pounds will she get?
French wine
20.93 f
Swiss cheese
1357 f
Chocolate
5566 f
Pegasys 2013
Measurements(length)
1. Write down 2 things that would be measured using:
(a) centimetres
(b) kilometres
(c) metres
(d) millimetres
2. What unit would you use to measure:
(a) the height of the classroom:
(b) the width of a 5p coin:
(c) the distance from the Earth to the Moon:
(d) the length of you arm:
3. The main instruments we use to measure length are:
ruler tape measure metre stick trundle wheel
Write down which one you would use to measure each of the following:
(a) the distance round a football pitch
(b) the length of a pair of trousers
(c) the width of your hand
(d) the length of your bedroom
4. Write down one more object that you would measure using:
(a) a trundle wheel:
(b) a ruler:
Pegasys 2013
5. Measure the length of these lines writing your answers in centimetres and in millimetres:
(a) (b)
(c) (d)
6. Measure these objects and write your answer in centimetres:
(a) (b)
(c) (d)
Pegasys 2013
Measurements (volume and capacity)
1. Which unit would you use to measure the following:
(a) The weight of a bag of crisps.
(b) The volume of a car’s petrol tank.
(c) The weight of a car.
(d) The volume of a medicine spoon.
2. Here are 5 items which all have different weights. Put them into order of weight starting
with the one you think is the lightest:
(a) a football
(b) a golf ball
(c) a cricket ball
(d) a tennis ball
(e) a ten-pin bowling ball
3. Here are 5 containers. Put them in order of the amount of liquid they can hold starting
with the one which you think holds the most:
(a) a baby bath
(b) a cup of coffee
(c) a small bottle of perfume
(d) a kettle
(e) a car’s petrol tank
Choose from:
Grams
Kilograms
Millilitres
Litres
Pegasys 2013
Measurements again (you may write on parts of this sheet)
1. A bag of apples weighs 175kg.(A)
A tin of beans weighs 500g. (B)
Mark these weights on the scales
shown using the letters A and B.
2. A bag of sugar weighs 1kg. (C)
A pack of flour weighs 2500g. (D)
Mark these weights on the scales
shown using the letters Cand D
3. The width of my calculator is 67cm. (E) The length of my middle finger is 75mm. (F)
Mark these measurements on this ruler using the letters E and F.
4. The width of a postcard is 95cm. (G) The length of a baby’s foot is 77mm. (H)
Mark these measurements on this ruler using the letters G and H.
5. (a) Mr Jones told his (b) A small can of
Science class to juice holds 150ml.
measure 225ml
of water. Shade this measure
to show 150ml.
Shade this measure
to show 225ml.
50
100
150
200
250
50
100
150
200
250
1kg 3kg
4kg 0
2kg
1kg 3kg
4kg 0
2kg
Pegasys 2013
(c) Mr Kemp told his (d) A small up
Science class to holds 175ml.
measure 25ml
of water. Shade this measure
to show 175ml.
Shade this measure
to show 25ml.
6. (a) Write down the length of this line:
(b) Extend the line so that is measures 92cm.
(c) What length of line have you added?
7. (a) Write down the length of this line:
(b) Extend the line so that is measures 73cm.
(c) What length of line have you added?
8. (a) Write down the length of this line:
(b) Reduce the line so that is measures 26cm.
(c) What length of line have you taken away?
50
100
150
200
250
50
100
150
200
250
Pegasys 2013
9. Write down the weight indicated on each of these scales?
10. Write down the volumes indicated on these measuring jugs:
(a) (b) (c)
40
80
120
160
200
50
100
150
200
250
20
40
60
80
100
(a) (b)
1kg 3kg
4kg 0
2kg
1kg 3kg
4kg 0
2kg
(c)
0·1kg 0·3kg
0·4kg 0
0·2kg
0·1kg 0·3kg
0·4kg 0
0·2kg (d)
(e) 0·4kg 1·2kg
1·6kg 0
0·8kg
0·4kg 1·2kg
1·8kg 0
0·8kg
(f)
Pegasys 2013
11. Estimate the size of these angles and then use a protractor to check:
(a) (b)
(c) (d)
(e) (f)
(g) (h)
(i) (j)
Pegasys 2013
Conversions
1. Change to kilograms:
(a) 4000g (b) 34000g (c) 90000g (d) 36000g
(e) 3500g (f) 4800g (g) 3700g (h) 2600g
(i) 3670g (j) 8635g (k) 2082g (l) 1070g
(m) 340g (n) 780g (o) 375g (p) 863g
(q) 65g (r) 23g (s) 99g (t) 21g
(u) 3g (v) 7g (w) 9g (x) 1g
2. Change to grams:
(a) 8kg (b) 19kg (c) 50kg (d) 75kg
(e) 4۰642kg (f) 1۰635kg (g) 7۰482kg (h) 1۰077kg
(i) 0۰349kg (j) 0۰653kg (k) 0۰42kg (l) 0۰68kg
(m) 3۰54kg (n) 5۰65kg (o) 10۰02kg (p) 16۰67kg
(q) 4۰8kg (r) 7۰2kg (s) 45۰4kg (t) 21۰6kg
(u) 0۰53kg (v) 0۰087kg (w) 0۰09kg (x) 0۰001g
3. Change these to litres:
(a) 3000ml (b) 3800ml (c) 60000ml (d) 83000ml
(e) 6700ml (f) 2700ml (g) 1700ml (h) 9200ml
(i) 3890ml (j) 3728ml (k) 5087ml (l) 2085ml
(m) 810ml (n) 270ml (o) 281ml (p) 928ml
(q) 29ml (r) 10ml (s) 82ml (t) 94ml
(u) 6ml (v) 1ml (w) 7ml (x) 4ml
Pegasys 2013
4. Change these to millilitres:
(a) 4l (b) 22l (c) 80l (d) 65l
(e) 4۰642l (f) 1۰635l (g) 7۰482l (h) 1۰077l
(i) 0۰756l (j) 0۰831l (k) 0۰81l (l) 0۰62l
(m) 1۰57l (n) 2۰91l (o) 12۰09l (p) 24۰27l
(q) 1۰3l (r) 6۰9l (s) 21۰1l (t) 98۰1l
(u) 0۰076l (v) 0۰722l (w) 0۰06l (x) 0۰005l
5. Change these to metres:
(a) 400cm (b) 300cm (c) 1200cm (d) 11400cm
(e) 60cm (f) 70cm (g) 91cm (h) 28cm
(i) 5230cm (j) 2871cm (k) 1009cm (l) 3322cm
(m) 8cm (n) 7cm (o) 1cm (p) 5cm
6. Change these to centimetres:
(a) 7m (b) 36m (c) 120m (d) 134m
(e) 570m (f) 23m (g) 12۰3m (h) 9۰06m
(i) 6۰4m (j) 0۰6m (k) 2۰05m (l) 7۰8m
(m) 7۰98m (n) 4۰007m (o) 0۰09m (p) 0۰7m
7. Change these to centimetres:
(a) 7000mm (b) 3600mm (c) 10200mm (d) 11400mm
(e) 570mm (f) 230mm (g) 123mm (h) 906mm
(i) 60mm (j) 20mm (k) 25mm (l) 78mm
(m) 7mm (n) 4mm (o) 2mm (p) 1mm
8. Change to millimetres:
(a) 8cm (b) 3cm (c) 6۰7cm (d) 6۰98cm
(e) 0۰34cm (f) 1۰78cm (g) 2۰59cm (h) 3۰09cm
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9. Change to kilometres:
(a) 6000m (b) 1500m (c) 29000m (d) 4870m
(e) 536m (f) 650m (g) 21m (h) 7m
10. Change to metres:
(a) 3km (b) 12km (c) 3۰8km (d) 4۰67km
(e) 0216km (f) 0۰64km (g) 0۰37km (h) 0۰017km
11. Change these to metres:
(a) 7000mm (b) 3600mm (c) 10200mm (d) 11400mm
(e) 570mm (f) 230mm (g) 123mm (h) 906mm
(i) 60mm (j) 20mm (k) 25mm (l) 78mm
(m) 7mm (n) 4mm (o) 2mm (p) 1mm
12. Change to millimetres:
(a) 9m (b) 2m (c) 3۰3m (d) 5۰34m
(e) 0234m (f) 0۰78m (g) 0۰99m (h) 0۰009m
13. Change to kilometres:
(a) 700000cm (b) 150000cm (c) 230000cm (d) 56700cm
(e) 53610cm (f) 4700cm (g) 660cm (h) 90cm
14. Change to centimetres:
(a) 2km (b) 23km (c) 3۰5km (d) 1۰53km
(e) 0333km (f) 0۰674km (g) 0۰557km (h) 0۰046km
Pegasys 2013
Interpret graphical data and situations involving probability to solve,
straightforward real-life problems involving money/time/measurement
Reading Tables
1. This table shows the cost of hiring a bike in Millport:
2 hours 4 hours 6 hours
Adult £3 £5.50 £6.75
Child £2 £3.50 £4.75
Answer the following questions from the table:
(a) How much does it cost for an adult to hire a bike for 4 hours?
(b) How much would it cost for 1 adult and 1 child to hire a bike for 2 hours?
(c) Mr and Mrs Cameron and their 2 young children want to hire bikes for 6 hours
How much would it cost altogether?
2. Here is a table showing the cost of a holiday in Spain. Prices are for 14 nights for an adult.
Children (5 – 15) pay half price.
June July August September October
£549 £589 £628 £607 £555
Answer these questions from the table:
(a) How much would it cost one adult to go to Spain in August?
(b) David is 21 and decides to take his little sister (15) to Spain in October.
How much would it cost altogether?
(c) Mr and Mrs Davis take Peter (10) and Pat (17) to Spain in July.
How much would this holiday cost in total?
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3.
M T W T F S S
1 2 3 4 5
6 7 8 9 10 11 12
13 14 15 16 17 18 19
20 21 22 23 24 25 26
27 28 29 30 31
Answer these questions about this calendar:
(a) What date was the third Sunday of October?
(b) The school had a Disco on October 23rd
.On which day of the week was it?
(c) The Douglas family went away on a skiing holiday on the 12th
and came home on
the23rd
. How many nights were they away for?
(d) What date was it 1 week before the 14th
?
4.
OCTOBER
BEETON
CEETON
DEETON
GEETON
LEETON
FEETON
34 21 24 9 13
41 25 3 22
7 27 33
17 32
30
ALL DISTANCES ARE IN KILOMETRES.
Answer these questions from the distance table:
(a) How far is from Beeton to Ceeton?
(b) Katie travelled from Leeton to Deeton.
How far did she travel?
(c) John drove from Beeton to Feeton and then
on to Geeton?
How far did he drive altogether?
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5. The local stationers make photocopies. The table shows the charges they make for doing
this:
NO OF
COPIES
BLACK &
WHITE COLOUR
UP TO 10 10p each 20p each
11-50 9p each 18p each
51-100 8p each 16p each
101-150 7p each 14p each
151-200 6p each 12p each
201-250 5p each 10p each
(a) How much would it cost for:
(i) 5 copies (ii) 60 copies (iii) 200 copies (iv) 105 copies
(black and white) (colour) (colour) (black and white)
(b) Janine wanted 50 copies of a worksheet in black and white but thought it might be
cheaper to get 55 copies.
By calculating the cost of 50 and 55 decide whether Janine was correct or not.
(c) Holly went to get 20 coloured copies of a photograph. How much would she have
saved if she had got black and white copies instead of coloured ones?
6. Mandy works in a shoe shop and is often asked about continental shoe sizes. She has
this table to help her:
Write out what continental sizes these U.K. sizes are the same as:
(a) 5 (b) 7 (c) 3·5
Continental 35·5 36 37 37·5 38 38·5 39 40 41 42 43
U.K. 3 3·5 4 4·5 5 4·5 6 6·5 7 8 9
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7. This table shows the number of rolls of wallpaper required for different sizes of rooms:
Height from ceiling to
floor
Width round room
9m 10m 12m 13m 14m 15m 17m 18m
0·75 – 1·00m 2 3 3 3 3 4 4 4
1·00 – 1·25m 3 3 4 4 4 5 5 5
1·25 – 1·50m 3 4 4 5 5 5 6 6
1·50 – 1·75m 4 4 5 5 6 6 6 7
1·75 – 2·00m 4 5 5 6 6 7 7 8
2·00 – 2·15m 4 5 5 6 6 7 7 8
2·15 – 2·38m 4 5 5 6 6 7 7 8
(a) Use the table to decide how many rolls of wallpaper would be needed for these
rooms:
(i) Height: 1·7m Width: 13m
(ii) Height: 2·1m Width: 18m
(iii) Height: 1·9m Width: 9m
(b) Mr and Mrs Baillie were going to wallpaper their lounge and their bedroom.
Their lounge was 2·2 metres high and had a width of 18m. Their bedroom was the
same height but was only 14 metres wide.
Work out how many rolls of paper they would need altogether.
(c) The wallpaper they chose for the lounge cost £12.50 a roll and for the bedroom
£7.75 a roll.
Calculate how much it would cost them to buy the wallpaper for both rooms.
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8. A survey was carried out amongst 500 adults who booked a holiday on-line to find out
what type of holiday they had chosen.
The results of the survey are shown in the table below.
Answer these questions from the table:
(a) How many of the adults surveyed were over 50 years old?
(b) How many adults under 50 booked to go on a cruise?
(c) How many in total booked to go on a package holiday?
(d) What does this information tell you about their holiday choices as people get older?
9. The loan table below shows the monthly repayments for borrowing different amounts from
a finance company with and without loan protection.
Answer the questions below from the information in the table.
(a) Ally wants to borrow £15000 and to pay it back over 24 months with loan
protection.
How much would he have to pay back each month?
(b) How much would he save per month if he took the loan without loan protection?
Age Package Activity Fly drive Cruise
50 and
under 112 96 38 24
Over 50 55 48 31 96
Sink Before You Can Swim Loans
48 months 36 months 24 months
with without with without with without
£20 000 492.27 476.66 633.62 601.94 889.81 845.32
£15 000 398.70 387.76 485.20 460.21 682.36 648.24
£10 000 279.14 265.18 346.81 329.47 494.91 470.16
£8 000 223.00 212.50 277.50 263.00 405.50 385.50
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(c) Stuart borrowed £10000 and wanted to pay it back over 36 months without loan
protection.
What is the amount he would have to pay per month?
(d) Gordon is paying back £263 per month without loan protection.
How much did he borrow, how long will it take him to pay the loan back and did he
take it with or without loan protection?
(e) Katie can repay £390 per month and wants to have loan protection.
What is the maximum amount of money she can borrow and for how long?
(f) If Katie decided not to take loan protection, how much could she then borrow and
for how long?
10. Maria decides to apply for a credit card and compares some of those available.
(a) How much is the annual fee for Canadian Express?
(b) What is the APR for National Direct?
(c) What is the monthly rate of interest for Vista?
(d) What is the minimum payment for Silvercarp?
(e) If Maria spent £150, how much would her minimum payment be with Vista?
(f) How much would it be with Silvercarp?
Credit Card Annual Fee APR Monthly rate Minimum
Payment
Vista £12 21·1% 1·61% £5 or 5%
Silvercarp none 19·8% 1·52% £4 or 4%
Canadian Express £15 28·8% 2·13% £5 or 5%
National Direct £10 18·6% 1·43% £5 or 5%
(which ever is
greater)
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11. The table below shows the cost of a touring holiday to USA with a stay in either Scottsdale
or Las Vegas. Prices are per person.
Dates
Days Apr 15 Apr 22
May 20
Jun 3 Jun 10
Sep 2, 9,
23 Sep 30 Oct 14
Tour +
Scottsdale 16 1965 2035 1999 2059 2069 2115 2039
Tour + Las
Vegas 17 2125 2189 2159 2219 2229 2269 2195
There is a supplement for single travellers of £495. Children 5 – 15 get 10% discount.
(a) How many days does the Tour and Scottsdale holiday last?
(b) How much would it cost for these holidays?
(i) Tour + Las Vegas leaving on June 10th
for 2 adults.
(ii) Tour + Scottsdale leaving on April 22nd
for 4 adults.
(iii) Tour + Las Vegas for 2 adults and 2 children (5 and 10) leaving on
October 14th
(iv) Tour + Scottsdale for 1 adult leaving on June 3rd
.
12. This table shows the cost of a holiday to Dubrovnik. Prices are per person.
Dates
Days Feb 7 Mar 7 Apr 4 May 2 Jun 6 Jul 4 Aug 1
Hotel Imperial 3 386 386 618 699 843 743 775
7 574 574 062 1123 1327 1279 1311
10 715 715 1220 1441 1690 1681 1713
14 903 903 1564 1865 2174 2217 2249
Hotel Excelsior 3 392 392 603 621 765 632 703
7 588 588 927 941 1145 1059 1143
10 735 735 1170 1181 1430 1389 1473
14 931 931 1494 1546 1810 1829 1913
There is a supplement for single travellers of £75 per night. Children 5 – 15 get 20% discount.
Calculate the cost of these holidays
(a) 14 nights in the Hotel Imperial for 2 adults leaving on June 6th
.
(b) 10 nights in Hotel Excelsior for 2 adults leaving on August 1st.
(c) 3 nights for 2 adults and 1 child in the Hotel Imperial leaving on April 4th
.
(d) 7 nights in the Hotel Excelsior for 1 adult leaving on March 7th.
Pegasys 2013
Interpreting statistical diagrams
1. A school tuck shop records how many packets of each flavour of crisps it sells each day.
The results for Monday are shown in the bar graph below.
(a) How many flavours of crisps does the
tuck shop sell?
(b) What is the most popular flavour?
(c) What was the total number of packets
sold?
(d) What is the least popular flavour?
(e) List the flavours in order from the
most popular to the least popular.
2. The bar chart shows the number
of hours of sunshine for a week
in April.
(a) Which day was the sunniest?
(b) Which day had 8 hours of
sunshine?
(c) What was the total number of hours
of sunshine over the weekend
(Saturday & Sunday)?
2
4
6
8
10
12
14
16
18
20
22
Nu
mb
er o
f p
ack
ets
so
ld
Nu
mb
er o
f h
ou
rs
2
4
6
8
10
12
14
Sun Mon Tue Wed Thu Fri Sat
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3.
A number of families in an estate were asked
about the number of children in the family.
The results are shown in the bar chart.
(a) How many families had 3 children?
(b) How many had no children?
(c) How many had more than 3 children?
(d) How many families were asked?
Number of children
Nu
mb
er o
f fa
mil
ies
1 0 2 3 4 5
1
2
3
4
5
6
7
8
9
4. 1200 books in the school library are
classified in four categories.
(a) What fraction of the books are
(i) fiction
(ii) non-fiction
(iii) reference
(iv) careers?
(b) How may non-fiction books
are there ?
(c) How many careers books are
there?
5. The 40 films on TV over a
holiday weekend can be put
into 4 categories.
(a) What fraction of the films were
(i) comedy
(ii) action
(iii) romance
(iv) cartoon ?
(b) Which category had the most
films?
c. How many comedy films were
there?
FICTION
NON-
FICTION
RE
FE
RE
NC
E
CA
RE
ER
S
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7. The line graph shows the average daily
hours of sunshine in a holiday resort in
the low season.
(a) Which month has the fewest hours
of sunshine ?
(b) What is the average daily hours of
sunshine in
(i) December
(ii) April?
(c) How many more hours of sunshine
are there in March than in November?
(d) Describe the general trend of the graph.
8. The graph shows the time taken
for a pupil to successfully walk through a
maze in 10 attempts.
(a) What happens as the number of
attempts increases?
(b) Why do you think that is the case?
6. A class of 30 pupils was asked
about how they travelled to school.
(a) What fraction
(i) walked
(ii) came by bus
(iii) came by car
(iv) cycled?
(b) What was the least popular
method of travel?
(c) How many came by bus?
hou
rs
1
2
3
4
5
6
7
8
9
10
11
Oct Nov Dec Jan Feb Mar Apr
25
30
35
40
1 2 3 4 5 6 7 8 9 10
Attempt
Tim
e (s
eco
nd
s)
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9. The graph shows the increase in a
baby’s weight over its first few weeks.
(a) What was the baby’s birth weight?
(b) What did it weigh after
(i) 5 weeks
(ii) 9 weeks
(iii) 12 weeks
(c) How much weight did the baby put
on between week 3 and week 7?
(d) Between which 2 consecutive
weeks was the greatest increase
in weight?
10. A sample of tomato plants are measured for height. Their heights are recorded
to the nearest centimetre.
The stem-and-leaf diagram shows the results.
(a) How many plants were in the sample?
(b) What height is the tallest plant?
(c) Write out level 5 in full.
(d) What fraction of the plants were more
than 50cm tall?
Height of Plant (cm)
2 1 3
3 0 2 2 7
4 4 5 6 8 9 9
5 6 7 9
6 3
n = 16 2 1 represents 21cm
week
wei
gh
t in
kg
2
3
4
5
6
0 1 2 3 4 5 6 7 8 9 10 11 12
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11. Susan decided to visit various shops in her surrounding area in order to
compare the price of an identical CD player.
Her results, shown below, are given to the nearest pound.
£68 £75 £73 £80 £75 £79 £81 £66 £71 £92 £83 £75 £78
(a) Construct a stem-and-leaf diagram to represent this data.
(b) What was the median price?
12. A factory has a small workforce of eleven people. The owner decides to compare absence
rates (in days) over the last two years.
The results are shown in the back-to-back stem-and-leaf diagram below.
(a) What is the largest number of absences recorded?
(b) State the median of the absences for "last year" and "this year".
(c) Compare the absences and comment
Absences (days)
last year this year
7 6 0 3 9 9
5 1 1 1 7
8 5 1 2 4 6
7 2 0 3 3
4 2 4 1 5
n = 11 0 3 represents 3 days n = 11
Pegasys 2013
Interpret Statistics
1. Two makes of matches are being compared, "Brighto" and "Sparky", they both cost the
same per box.
14 boxes of each type are sampled to find the number of matches in a box. Here are the
results.
Brighto Sparky
(a) Construct a back-to-back stem-and-leaf diagram to represent this information.
(b) Which make of match, if any, is a better buy? Give a reason for your answer.
2. Paul works in a shoe shop on a Saturday. The manager wants to make a special purchase
of "Trainers". He asked Paul to do a tally of sizes of men's shoes sold that day.
Size
PairsSold
6 6 7 7 8 9 10
5 17 21 16 15 11 2
12
12
(a) Which size of shoe will the manager order most of?
(b) What do we call this measure in statistics?
3. The Lucky Strike Match Company advertises the average contents of its boxes as 48.
Here is a sample of the boxes contents :
45 47 46 50 48 51 46 47 49 51
Is the company correct in their advert? Give a reason for your answer.
4. The ages of the players in a local football team are given below :
19 23 25 24 19 25
31 27 29 30 34
(a) Calculate the mean, median and mode.
(b) Jake is 25 years old. Is he above or below the average age?
(c) The two oldest players leave and are replaced by two players aged 18 and 25.
Calculate the mean median and modal age of the team now.
(d) How would you describe Jake's age now?
48 45 47 39 52 36 58
41 38 39 46 50 61 37
38 42 49 39 62 56 52
40 58 49 29 51 64 57
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5. A small firm employs 10 people. The salaries of the employees are as follows :
£40 000, £18000, £15000, £9000, £15000, £15000, £13000, £15000, £15000, £15000.
(a) Calculate the mean, median and mode.
(b) Which of the three measures best describes the average salary in the company?
6. Diane does a lot of travelling in her job. She keeps a note of the miles she drove each
week for the first 10 weeks.
785 846 816 704 685 723 960 788 729 814
(a) Calculate the mean weekly mileage.
(b) If Diane's mean weekly mileage stays the same, how many miles would she
expect to travel in a year? (She has 6 weeks holiday when she does no driving)
7. In a 5-a-side football competition, the average age of a team must not exceed 16.
Below are the ages of 2 groups of 10 players who want to enter 2 teams each.
A : 14 , 16 , 14 ,17 , 15 , 18 , 16 , 15 , 17 , 18
B : 14 , 15 , 16 , 17 , 15 , 16 , 14 , 16 , 18 , 14
(a) How would you arrange the teams?
(b) Here are the ages of another team: 15, 17, 16, 17, 16
Will they be allowed to take part in the competition?
8. In nine arithmetic tests during the term, Peter's scores were:
20 22 18 21 22 16 14 19 17
Which of the three averages - mean, median or mode - would he prefer to count as his
'mark' ?
9. The first eight customers at a supermarket one Saturday
spent the following amounts:
£25.10, £3.80, £20.50, £15.70,
£38.40, £9.60, £46.20, £10.46.
(a) Find the mean amount spent.
(b) I spend £11.53. Compare this to the average amount spent.
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Probability
In each of these situations, decide which is the more likely to happen. Give a reason for you
choice each time.
1. (a) A: choosing a red card from a pack of cards
B: throwing a multiple of 3 on a die
(b) A: choosing a double from a set of dominoes
B: choosing a face card from a pack of cards
(c) A: throwing an even number on a die
B: getting a head when a coin is tossed
(d) A: choosing an ace from a pack of cards
B: getting a number more than 10 when throwing 2 dice
(e) A: getting a total of more than 7 when two dice are thrown
B: getting ‘tails’ when a coin is tossed
(f) A: choosing a face card from a pack of cards
B: choosing a club from a pack of cards
2. (a) A coin is tossed 80 times. How many times would you expect:
(i) heads (ii) tails?
(b) A die is thrown 24 times. How many times would you expect:
(i) an even number (ii) a 3?
(c) A card is chosen from a pack of playing cards 156 times. The card is replaced each
time. How many times would you expect:
(i) a club (ii) a face card (iii) the ace of clubs?
(d) A domino is chosen from a pack 112 times and replaced each time. How many
times would you expect:
(i) a double (ii) a domino with 4 spots (iii) a double 4?
3. The probability of a bus arriving on time at a certain bus stop is 4
1 .
(a) What is the probability of it not arriving on time?
(b) Out of 64 buses arriving at that bus stop, how many are likely to be on time?
4. The probability of a cat having a litter of more than eight kittens is 240 .
(a) What is the probability of a cat having a litter of eight or less kittens?
(b) Out of 75 female cats, how many would you expect to have a litter of more than
eight kittens?
Pegasys 2013
ANSWERS
Four Rules
1. (a) 9862 (b) 4785 (c) 2056 (d) 716 rem 5
2. (a) 8194 (b) 842
3. 1261 4. 87
5. (a) £37.87 (b) £12.13
6. £258 7. £352.75
8. £3744 9. 26 classes
10. 64 packs 11. (a) 4 cans (b) 10p
12. (a) 8 teams (b) 4 people
13. 27 rows with 5 plants over
14. £4.45 15. (a) £19.40 (b) 34 weeks
16. £1.14 short 17. £565
18. £2.55 19. £55
20. £131 21. £130
22. £1090 23. World of Computers by £5
24. £64 25. £56
26. £14.28 27. £4.35
28. £192.50 29. £8.95
30. (a) £49.59 (b) no (c) £1.59 short
31. £6000 32. (a) 65p (b) £97.50
33. £3.84 34. (a) £375 (b) £62.50
35. 50p 36. £23.10
37. £22 38. £1372
39. (a) 18 boxes (b) 15 tiles over
40. 54·1kg; 52·5kg; 52·9kg; 52kg
41. 12 weeks 42. Wally
43. (a) £5.19 (b) £4.22
44. (a) 9·78km (b) 7·22km
Adding and subtracting negative numbers
1. (a) 1 (b) 5 (c) 3 (d) 8 (e) 2 (f) 7
(g) 4 (h) 10 (i) 5 (j) 6 (k) 5 (l) 4
(m) 1 (n) 13 (o) 1 (p) 1
2. (a) 10 (b) 50 (c) 40 (d) 70 (e) 10 (f) 5
(g) 42 (h) 16 (i) 23 (j) 36 (k) 0 (l) 70
(m) 23 (n) 27 (o) 71 (p) 99
3. 4oC 4. £5
5. 59 oC 6. 6
oC
7. 79 years 8. C A B
Percentages
1. (a) £45 (b) £90 (c) £22.50 (d) £27
(e) £85.50 (f) £9 (g) £180 (h) £135
(i) £207 (j) £801 (k) £247.50 (l) £165.60
(m) £89.10 (n) £60.30 (o) £20.70 (p) £115.20
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2. (a) £59.50 (b) £21.25 (c) £83.30 (d) £36.55
(e) £102 (f) £42.50 (g) £65.45 (h) £96.90
(i) £65.28 (j) £78.71 (k) £46.92 (l) £115.94
(m) £18.87 (n) £30.09 (o) £53.38 (p) £85.51
3. (a) £20 (b) £6 (c) £10 (d) £14
(e) £50 (f) £36 (g) £18 (h) £80
(i) £16.40 (j) £15.20 (k) £18.80 (l) £27.60
(m) £20.80 (n) £44.40 (o) £13.60 (p) £7.20
4. (a) £120 (b) £60 (c) £96 (d) £36
(e) £54 (f) £300 (g) £840 (h) £2400
(i) £12000 (j) £204 (k) £339.60 (l) £58.80
(m) £166.80 (n) £26.40 (o) £2394 (p) £9
VAT
1. £288 2. £15.12 3. £432 4. £100.20
5. £89.04 6. £394.80
More percentages
1. (a) 10 (b) 78 (c) 11
2. 12; 15; 30
3. 311 4. (a) £202.50 (b) £54.28 (c) £694.20
5. 8·25 mins 6. 42g
7. £270 8. £220.40
9. (a) £24 (b) £40.50 (c) £192
10. 120 11. 140g
12. (a) 104 (b) 120 (c) 128
Percentages again
1. (a) 84%; 88%; 80%, 80%; 84%; 75%; 60%; 90% (b) Art
2. (a) 25% (b) 90% (c) 60% (d) 35%
(e) 50% (f) 35% (g) £70% (h) 40%
(i) 20% (j) 45% (k) 15% (l) 72%
(m) 55% (n) 10% (o) 80% (p) 25%
3. (a) 20% (b) 25% (c) 10%
(d) 40% (e) 20% (f) 4%
4. 25% 5. 90% 6. 65%
7. 48% 8. 45%
Pegasys 2013
Fractions, Decimals and Percentages (1)
1. (a) £32 (b) 13kg (c) £5.20 (d) 36cm
(e) £85 (f) 45·5g (g) £10.64 (h) 405kg
(i) £4.68 (j) £4.25 (k) 369mm (l) £0.81
(m) £1397 (n) 270 tonnes (o) 7·5kg
2. (a) £23.40 (b) 162g (c) £5.85 (d) 252kg
(e) £1.70 (f) 17·85cm (g) £12.16 (h) £17
(i) £572 (j) 360g (k) £200 (l) £338.40
(m) £1170 (n) £0.48 (o) 84 tonnes
3. (a) £4.75 (b) £3.05 (c) £1.14 (d) 42p
(e) £5.95 (f) 21p (g) £2.20 (h) £13.65
(i) £41.73 (j) £2.79 (k) £0.23 (l) 30p
(m) £1.09 (n) £0.36 (o) 55p
4. (a) 80% (b) 75% (c) 28% (d) 70%
(e) 17% (f) 95% (g) 56% (h) 27%
(i) 72% (j) 42% (k) 13% (l) 62%
(m) 7% (n) 43% (o) 19% (p) 10%
(q) 51% (r) 21%
5. (a)
Maths English Tech Science Art History French
75% 89% 62% 69% 83% 68% 66%
(b) English (c) Tech
Fractions, Decimals and Percentages (2)
1. (a) £287.50 (b) 184kg (c) 28·75cm (d) £41.40
(e) 2415g (f) 241·5oC (g) £9.20 (h) £4025
2. (a) £200 (b) 128kg (c) 20cm (d) £28.80
(e) 1680g (f) 168oC (g) £6.40 (h) £2800
Pegasys 2013
3.
Name Increase New Wage
John Hughes £9.20 £239.20
Steven Higgins £10.08 £178.08
Susan Marshal £8.40 £218.40
Stewart Aitken £2.90 £147.90
Pamela Grant £12.60 £372.60
Neil McShane £13.50 £238.50
James Mackie £18.80 £253.80
Lorna Graham £9.45 £219.45
Pat Lavery £23.40 £491.40
4. (a) 3
560% (b)
4
757% (c)
1
250% (d)
1
425%
(e) 11
1669% (f)
2
540% (g)
2
729%
5. (a) 36% (b) 56% (c) 43%
6. (a) 20% (b) 2% (c) 5%
Fractions, Decimals and Percentages (3)
1. (a) £46 (b) £29.60 (c) £91.20 (d) £13.60
(e) £130 (f) £26.80
2. (a) £276 (b) £177.60 (c) £547.20 (d) £81.60
(e) £780 (f) £160.80
3. (a) £92 (b) £2392 (c) £95.68
4. (a) £1105 (b) £23205 (c) £1160.25
5. £848.72 6. £898.88
Pegasys 2013
Fractions
1. (a) £15 (b) £32 (c) £5
(d) £46 (e) £32.40 (f) £6
2. (a) 210cm (b) 830ml (c) £94
3. 2·8m 4. 6 hours
5. 207 adults 6. 6 boys
7. 10 white chocolate 8. 6 white candles
9. (a) 36 (b) 216
10. 30 mins 11. 25 days 12. 16 hours
More fractions
1. (a) 192m (b) £160 (c) £192.50
2. 36 sweets 3. (a) 21 (b) 3
4. (a) 1160 (b) 290
5. (a) 16 (b) 12 (c) 8
6. (a) 60 (b) 15 (c) 25
7. 400 cars 8. 350 pieces 9. 28
Rounding – revision and 2 decimal places
1. (a) 3 (b) 6 (c) 1 (d) 8
(e) 8 (f) 3 (g) 5 (h) 9
(i) 2 (j) 8 (k) 6 (l) 1
(m) 5 (n) 8 (o) 4 (p) 6
2. (a) 12 (b) 35 (c) 28 (d) 83
(e) 18 (f) 38 (g) 36 (h) 90
(i) 123 (j) 364 (k) 19 (l) 343
(m) 45 (n) 218 (o) 74 (p) 119
3. (a) 20 (b) 70 (c) 70 (d) 90
(e) 60 (f) 30 (g) 20 (h) 90
(i) 60 (j) 80 (k) 20 (l) 50
(m) 30 (n) 80 (o) 70 (p) 30
4. (a) 210 (b) 130 (c) 760 (d) 340
(e) 280 (f) 120 (g) 520 (h) 200
(i) 110 (j) 560 (k) 140 (l) 500
(m) 430 (n) 180 (o) 260 (p) 310
5. (a) 300 (b) 200 (c) 300 (d) 800
(e) 700 (f) 400 (g) 500 (h) 900
(i) 100 (j) 300 (k) 700 (l) 700
(m) 500 (n) 200 (o) 200 (p) 800
(q) 1300 (r) 1400 (s) 2100 (t) 3500
(u) 1900 (v) 2000 (w) 6500 (x) 8100
Pegasys 2013
6.i. (a) 2910 (b) 5670 (c) 1460 (d) 8320
(e) 7770 (f) 3100 (g) 4520 (h) 9290
(i) 2130 (j) 7930 (k) 6250 (l) 1100
(m) 4770 (n) 8450 (o) 3940 (p) 6000
ii. (a) 2900 (b) 5700 (c) 1500 (d) 8300
(e) 7800 (f) 3100 (g) 4500 (h) 9300
(i) 2100 (j) 7900 (k) 6300 (l) 1100
(m) 4800 (n) 8500 (o) 3900 (p) 6000
iii. (a) 3000 (b) 6000 (c) 1000 (d) 8000
(e) 8000 (f) 3000 (g) 5000 (h) 9000
(i) 2000 (j) 8000 (k) 6000 (l) 1000
(m) 5000 (n) 8000 (o) 4000 (p) 6000
7. (a) 0·3 (b) 0·3 (c) 0·6 (d) 0·6
(e) 0·2 (f) 0·2 (g) 0·4 (h) 0·3
(i) 0·9 (j) 0·4 (k) 0·8 (l) 0·7
(m) 0·9 (n) 0·2 (o) 0·7 (p) 1·0
8. (a) 2·9 (b) 5·7 (c) 1·5 (d) 8·3
(e) 7·8 (f) 3·1 (g) 4·5 (h) 9·3
(i) 2·1 (j) 7·9 (k) 6·3 (l) 1·1
(m) 4·8 (n) 8·5 (o) 3·9 (p) 5·6
9. (a) 62·0 (b) 15·6 (c) 31·5 (d) 18·3
(e) 47·3 (f) 0·1 (g) 10·5 (h) 39·6
(i) 20·8 (j) 0·3 (k) 61·5 (l) 1·0
(m) 49·9 (n) 8·4 (o) 18·0 (p) 1·0
10. (a) 2·92 (b) 5·66 (c) 1·41 (d) 8·32
(e) 7·76 (f) 3·12 (g) 4·53 (h) 9.21
(i) 2·13 (j) 7·94 (k) 6·25 (l) 1·09
(m) 4·76 (n) 8·45 (o) 3·94 (p) 5·50
11. (a) £6.17 (b) £0.16 (c) 1·07 s (d) 57·14 miles
(e) 6·28 pages (f) £138.14 (g) £0.17 (h) 0·88 mins
(i) 2·93 cm (j) 0·36 km
Further rounding
1. (a) 4m (b) 324m (c) 290cm (d) 484cm
2. (a) 4cm (b) 7cm (c) 3cm
3. (a) £2.46 (b) £90.28 (c) £32.41 (d) £86.90
4. (a) £4.64 (b) £63.76 (c) £0.93 (d) £36.86
5. 38p 6. £1.83 7. £2.18
Pegasys 2013
ROUNDING – significant figures
1. (a) 20 (b) 6 (c) 80 (d) 30
(e) 100 (f) 300 (g) 300 (h) 800
(i) 8000 (j) 2000 (k) 8000 (l) 5000
(m) 10 (n) 600 (o) 4 (p) 10000
(q) 1 (r) 100 (s) 0·9 (t) 600
2. (a) 8·7 (b) 93 (c) 0·19 (d) 680
(e) 2·1 (f) 6·5 (g) 31 (h) 26
(i) 24 (j) 19 (k) 6400 (l) 5·0
(m) 0·053 (n) 0·0061 (o) 0·087 (p) 14000
(q) 2·5 (r) 45000 (s) 29 (t) 0·76
3. (a) 120 (b) 4·0 (c) 250 (d) 41
(e) 49 (f) 0·49 (g) 3·8 (h) 0·084
(i) 250 (j) 17 (k) 500 (l) 65
Calculate distance given speed and time
1. (a) 150 (b) 160 (c) 120 (d) 90 (e) 240 (f) 374
(g) 384 (h) 208 (i) 288 (j) 192 (k) 168 (l) 220
2. (a) 125 (b) 54 (c) 224 (d) 210 (e) 105 (f) 105
(g) 279 (h) 95 (i) 81 (j) 168 (k) 168 (l) 252
3. (a) 200km (b) 390 miles (c) 217·5km (d) 12km (e) 24miles
4. (a) 3220km (b) Yes ( max. distance 5980km)
5. (a) 91km (b) 28 + 126 + 21 = 175km
EXTENSION – calculating speed and time
1. (a) 60 (b) 50 (c) 80 (d) 65 (e) 100 (f) 72
(g) 46 (h) 76 (i) 56 (j) 65 (k) 83 (l) 51
2. (a) 50 (b) 64 (c) 82 (d) 76 (e) 64 (f) 66
(g) 68 (h) 54 (i) 38 (j) 60 (k) 48 (l) 42
3. (a) 6 (b) 12 (c) 10 (d) 9 (e) 3 (f) 5
(g) 2 (h) 6 (i) 7 (j) 3 (k) 7 (l) 4
4. (a) 8 (b) 5 (c) 10 (d) 8 (e) 6 (f) 7
(g) 2 ½ (h) 3 ½ (i) 1 ½ (j) 2·4 (k) 6·4 (l) 5·5
Time Intervals (12 hour time)
1. (a) 4 (b) 6 (c) 3 (d) 8 (e) 10 (f) 1
(g) 4 (h) 8 (i) 9 (j) 8 (k) 12 (l) 8
2. (a) 3 h 30 min (b) 2 h 15 min (c) 3 h 30 min (d) 1 h 30 min
(e) 2 h 15 min (f) 2 h 45 min (g) 1 h 45 min (h) 6 h 45 min
(i) 6 h 15 min (j) 9 h 15 min (k) 10 h 45 min (l) 13 h 30 min
3. (a) 5 hrs (b) 14 hrs (c) 15 hrs (s) 20 hrs
(e) 9 hrs (f) 5 hrs (g) 3 hrs (h) 7h15m
(i) 3 hrs (j) 8h15m (k) 12h15m (l) 3h45m
4. 30 min 5. 8 ½ hrs 6. 1 ½ hrs 7. 8h 45m 8. 15h 45m
Pegasys 2013
9. (a) 1.52 p.m. (b) 3.09 p.m. (c) 4.37 a.m.
(d) 5.50 a.m. (e) midnight (f) 7.23 a.m.
10. (a) 3.05 p.m. (b) 7.55 p.m. (c) 5.25 a.m.
(d) 3.15 a.m. (e) 2.16 p.m. (f) 1.37 a.m.
11. (a) 3.30 p.m. (b) 11.15 a.m. (c) 7.15 p.m.
(d) 8 a.m. (e) 9.29 a.m. (f) 6 a.m.
12. (a) 9.45 a.m. (b) 6.35 p.m. (c) 10.45 p.m.
(d) 2.40 a.m. (e) 11.30 p.m. (f) 10.30 a.m.
13. (a) 4 p.m. (b) 6 a.m. (c) 11.05 p.m.
(d) 10.06 p.m. (e) 5.20 p.m. (f) 2.20 a.m.
14. (a) 2.15 p.m. (b) 00.35 a.m. (c) 11.45 p.m.
(d) 1.52 p.m. (e) 6.45 a.m. (f) 2.18 a.m.
15. (a) 2.15 p.m. (b) 12.10 p.m. (c) 4.05 p.m.
Time Intervals (24 hour time)
1. (a) 35 (b) 25 (c) 20
(d) 24 (e) 34 (f) 32
2. (a) 12 (b) 4 (c) 12
(d) 18 (e) 15 (f) 13
3. (a) 2 hours 10 mins (b) 2 hours 20 mins (c) 1 hour 45 mins
(d) 15 hours 20 mins (e) 15 hours 20 mins (f) 2 hours 45 mins
4. (a) 0948 (b) 1356 (c) 1710 (d) 1805 (e) 1223 (f) 1901
5. (a) 1310 (b) 1210 (c) 1515 (d) 2250 (e) 2025 (f) 1145
6. (a) 2300 (b) 1708 (c) 0615 (d) 0323 (e) 0731 (f) 2235
7. (a) 2000 (b) 1234 (c) 1009 (d) 2230 (e) 0250 (f) 2206
8. (a) 0800 (b) 1435 (c) 2305 (d) 1847 (e) 1938 (f) 1722
9. (a) 1120 (b) 1205 (c) 1140 (d) 0957 (e) 1750 (f) 0139
10. 1120 11. 0710 12. (a) 2215 (b) miss start by 5 minutes
Timetables (1)
1. (a) 4 (b) depends on school
2. Art 3. Period 4 – P.E. 4. English
5. 1·40 p.m. 6. English 7. 15 mins
8. 45 mins 9. (a) 1.10 p.m. (b) 24 mins
10. 8.45 a.m. 11. 3.40 p.m.
12 (a) 10 mins (b) 50 mins
13. (a) 105 mins (b) 1 hour 45 mins
14. (a) 220 mins (b) 3 hours 40 mins
15. 55; 50; 55; 55 16. 1 hour 50 mins 17. 210 mins
18. 6 hours 30 mins 19. 32 hours 30 mins
20. (a) 1 hour 15 mins (b) 3 hours 45 mins (c) 27 hours 30 mins
21. (a) 8 hours 5 mins (b) 40 hours 25 mins
Pegasys 2013
Timetables (2)
1. BBC 1: Eastenders, Politics, Last of the Summer Wine, Songs of Praise, Sportscene
ITV 1: News, Eye to Eye. Gaelic Programme, Scotsport, Driving Miss Daisy
2. (a) Sportscene (b) 45 mins
3. (a) 5·50 p.m. (b) Scotsport
4. (a) News (b) Eastenders
5. (a) Eastenders (b) Driving Miss Daisy
6. (a) 25 mins (b) 55 mins (c) 80 mins (d) 1 hour 20 mins
7. (a) 45 mins (b) 30 mins (c) 1 hour 15 mins
8. (a) 30 mins (b) Seven Days
9. 25 mins
10. (a) 1 hour 55 mins; 40 mins; 45 mins (b) 3 hours 20 mins
11. (a) 1hour 45 mins (b) 2 hours 45 mins (c) Sportscene (d) 4 hours 30 mins
Timetables (3)
1. (a) 30 mins (b) 2 hours (c) 45 mins
(d) 1 hour 45 mins (e) 4 hours
2. 30 mins
3. 3 hours 30 mins
4. (a) 11·15 a.m. (b) 11·50 a.m. (c) 25 mins
5. (a) Abseiling (b) 105 mins
(c) 15 mins (d) 5 mile run, breakfast, planning for midnight hike
6. (a) 5·30 p.m. (b) 1 hour 30 mins (c) 7·30 p.m.
7. 12·45 a.m. / 3 hours 15 mins; 12·30 a.m. / 3 hours; 1·15 a.m. / 3 hours 45 mins
(a) Kieron (b) Daniel (c) 45 mins
Ratio(1)
1. (a) £15 : £35 (b) 24kg : 56kg
(c) £25 : £10 (d) 192g : 48g
2. (a) Harry £10; James £30; Bill £80
(b) Susan £8; Beth £20; Jill £28
3. (a) £2380 (b) £1860
4. 15 girls
5. (a) 16g (b) Dave £206; Frank £618
6. (a) 30 cows (b) 72 cows (c) Bill 27; Dan 36; George 9
Pegasys 2013
Ratio (2)
1. (a) £18:£30 (b) £70:£30 (c) £8:£48 (d) £40:£10
(e) £75:£45 (f) £40:£35 (g) £16:£20 (h) £100:£140
2. (a) £8:£24:£56 (b) £6:£9:£33 (c) £15:£20:£25 (d) £12:£24:£60
3. John £1360; David £2040
4. 20 girls
5. 21 bags of sand
6. (a) 40 dogs (b) 12 boys (c) 12 diamonds
(d) John £3600; Dave £6000
7. (a) Xena 40 coins; Joxar 8 coins
(b) 72 coins
(c) Xena 27 coins; Gabrielle 15 coins; Joxar 12 coins; Calisto 18 coins.
Volume of a cube and cuboid
1. (a) 27cm3 (b) 343cm
3 (c) 8cm
3 (d) 64cm
3
(e) 125cm3 (f) 1000cm
3 (g) 216cm
3 (h) 729cm
3
(i) 512cm3 (j) 2744cm
3 (k) 1331cm
3 (l) 8000cm
3
2. (a) 60cm3 (b) 42cm
3 (c) 280cm
3 (d) 48cm
3
(e) 1600mm3 (f) 53·9cm
3 (g) 0·36m
3 (h) 45cm
3
(i) 800cm3 (j) 600cm
3
3. (a) 120cm3 (b) 144cm
3 (c) 6m
3 (d) 2160cm
3
(e) 343cm3 (f) 360cm
3 (g) 224·1cm
3 (h) 357·76cm
3
(i) 510000mm3 (j) 7148·5cm
3
4. 7776 cm3 5. 31 pupils
6. (a) 300 000 000cm³ (b) 300 000 litres
Finding the area of a shape
1. 14 cm2 2. 30 cm
2 3. 54 cm
2 4. 188 cm
2
6. 380 cm2 6. 338 cm
2 7. 664 cm
2 8. 71·28 cm
2
9. 16 cm2
Finding the perimeter of a shape
1. (a) 16cm (b) 24cm (c) 38cm (d) 64cm
(e) 90cm (f) 104cm (g) 144cm (h) 55·6cm
(i) 60cm
2. (a) 73·8cm (b) 264cm (c) 133·4cm
(d) 58·2cm (e) 161·4m
Pegasys 2013
Calculate rate
1. (a) £4.49 (b) £3.50 (c) £0.32 (d) £9
(e) £0.15 (f) £8.50 (g) £0.89 (h) £0.19
2. (a) 65 miles (b) 24 km (c) 700 cars (d) 14 words
(e) 3 pints (f) 0·2 kg (g) £3.60 (h) 1·2 km
3. (a) 5kg pack (b) first car (c) Jim (d) Paula
(e) choc.eclair (f) doll (g) machine A
Best Buy
(a) 3 litres (b) 15 litres (c) 550g (d) 750g
(e) 0·7 litres (f) 500ml (g) 0·8kg (h) 600g
(i) Twin Pack (j) 550ml
Direct Proportion
1. (a) 2000 sheets (b) 90 p (c) 67·8 g (d) 910 kcal
(e) 84 m (f) 4200 ml (g) 400 p (h) 11.4Euros
2. (a) 700 (b) £2.25 (c) 7 kg (d) 110 km
(e) 17·1 cm (f) £164 (g) 3 hours (h) £190.75
(i) £504 (j) 3 ¼ hours (k) £56.25
3. (a) £60 (b) 175 miles
4. 65·6 km 5. 20·25 cm 6. 4·34 cm
7. 34 books 8. £2.56, £2.24, £2.25, £3.60, £0.48 Total = £11.13
Direct Proportion again
1. (a) 600g (b) 150g (c) 450g
2. (a) 42p (b) £1.26 (c) £4.62
3. 2·3kg
4. (a) £7.02 (b) 79·8mm (c) 22·8mm (d) 9kg
5. (a) £13.20 (b) £633.60
6. £258
7. 27 litres
8. 9 books
9. £124
Pegasys 2013
Hire Purchase
1. (a) (i) £369 (ii) £39 (b) (i) £135 (ii) £17
(c) (i) £305 (ii) £26 (d) (i) £424 (ii) £34
(e) (i) £566 (ii) £56 (f) (i) £474 (ii) £25
(g) (i) £325 (ii) £42 (h) (i) £550.40 (ii) £51.40
2. £561.95; £534.15; £510.35.
3. £120
4. (a) (i) £45 (ii) £501 (iii) £51
(b) (i) £78 (ii) £870 (iii) £90
(c) (i) £39 (ii) £240 (iii) £45
(d) (i) £55.55 (ii) £429.90 (iii) £59.90
(e) (i) £82 (ii) £499.60 (iii) £89.60
(f) (i) £138 (ii) £1077.60 (iii) £157.60
(g) (i) £821.25 (ii) £4157.25 (iii) £872.25
(h) (i) £22.90 (ii) £254.20 (iii) £25.20
5. £7200; £8240; £8496 - £1296 6. £120
Holiday Money (1)
1. (a) $7.75 (b) $48.05 (c) $716.10 (d) $31
(e) $68.20 (f) $13.95 (g) $320.85 (h) $55.80
(i) $100.75 (j) $6.98 (k) $132.55 (l) $27.13
2. (a) 4.64€; 600¥ (b) 56.84€; 7350¥ (c) 214.60€; 27750¥
(d) 34.80€; 4500¥ (e) 31.32€; 4050¥ (f) 8.12€; 1050¥
(g) 352.64€; 45600¥ (h) 60.32€; 7800¥ (i) 96.28€; 12450¥
(j) 11.60€; 1500¥ (k) 0.58€; 75¥ (l) 21.46€; 2775¥
3. (a) 10.20$ (b) 96.90$ (c) 32.30$ (d) 350.20$
(e) 229.50$ (f) 39.10$ (g) 3.40$ (h) 130.90$
(i) 57.80$ (j) 816$ (k) 0.85$ (l) 50.15$
4. 127.60€; 109.04€
5. (a) $852.50 (b) $52.50
6. (a) 11250¥ (b) 9830¥
Pegasys 2013
Holiday Money (2)
1. (a) £5 (b) £16 (c) £37 (d) £47
(e) £64 (f) £1030 (g) £214 (h) £1340
(i) £45.20 (j) £63.10 (k) £1094.30 (l) £7.25
2. (a) £30 (b) £52.50 (c) £270 (d) £97.50
(e) £750 (f) £1275 (g) £2625 (h) £14250
(i) £2460 (j) £1125 (k) £7.50 (l) £148.50
3. (a) £5.18 (b) £2.59 (c) £621.89 (d) £388.68
(e) £269.49 (f) £93.28 (g) £36.28 (h) £1036.49
(i) £24.88 (j) £9.87 (k) £64.26 (l) £4.66
4. £9.49; £14.63; £38.92
5. £9.99
6. (a) 3724R (b) 380R (c) £25
Measurements (length)
1. (a), (b), (c), (d) pupil’s own ideas
2. (a) m (b) mm (c) km (d) cm
3. (a) trundle wheel (b) tape measure (c) ruler (d) metre stick / tape measure
4. (a) and (b) pupil’s own ideas
5. (a) 6cm / 60mm (b) 7·3cm / 73mm
(c) 3·5cm / 35mm (d) 2·2cm / 22mm
6. (a) 6·1cm (b) 4·9cm (c) 8·4cm (d) 7·6cm
Measurements (volume and capacity)
1. (a) gram (b) litre (c) kilogram (d) millilitre
2. tennis ball, golf ball, football, cricket ball, ten-pin bowling ball
3. petrol tank, baby bath, kettle, cup of coffee, perfume bottle
Pegasys 2013
Measurements (volume and capacity)
1. weight marked 2. weight marked
3. length marked 4. length marked
5. volume marked
6. (a) 6·2cm (b) line extended (c) 3cm
7. (a) 3·7cm (b) line extended (c) 3·6cm
8. (a) 8·1cm (b) line reduced (c) 5·5cm
9. (a) 2·5kg (b) 1·25kg (c) 0·15kg
(d) 0·275kg (e) 1·3kg (f) 0·7kg
10. (a) 140ml (b) 125ml (c) 75ml
11. (a) 38o (b) 123
o (c) 105
o
(d) 53o (e) 25
o (f) 143
o
(g) 36o (h) 110
o (i) 16
o
(j) 114o
Conversions
1. (a) 4kg (b) 34kg (c) 90kg (d) 36kg
(e) 3·5kg (f) 4·8kg (g) 3·7kg (h) 2·6kg
(i) 3·67kg (j) 8·635kg (k) 2·082kg (l) 1·07kg (m) 0·34kg
(n) 0·78kg (o) 0·375kg (p) 0·863kg (q) 0·065kg (r)
0·023kg (s) 0·099kg (t) 0·021kg (u) 0·003kg (v)
0·007kg (w) 0·009kg (x) 0·001kg
2. (a) 8000g (b) 19000g (c) 50000g (d) 75000g
(e) 4642g (f) 1635g (g) 7482g (h) 1077g
(i) 349g (j) 653g (k) 420g (l) 680g
(m) 3540g (n) 5650g (o) 10020g (p) 16670g
(q) 4800g (r) 7200g (s) 45400g (t) 21600g
(u) 530g (v) 87g (w) 90g (x) 1g
3. (a) 3l (b) 3·8l (c) 60l (d) 83l
(e) 6·7l (f) 2·7l (g) 1·7l (h) 9·2l
(i) 3·89l (j) 3·728l (k) 5·087l (l) 2·085l
(m) 0·81l (n) 0·27l (o) 0·281l (p) 0·928l
(q) 0·029l (r) 0·01l (s) 0·082l (t) 0·094l
(u) 0·006l (v) 0·001l (w) 0·007l (x) 0·004l
Pegasys 2013
4. (a) 4000ml (b) 22000ml (c) 80000ml (d) 65000ml
(e) 4642ml (f) 1635ml (g) 7482ml (h) 1077ml
(i) 756ml (j) 831ml (k) 810ml (l) 620ml
(m) 1570ml (n) 2910ml (o) 12090ml (p) 24270ml
(q) 1300ml (r) 6900m (s) 21100ml (t) 98100ml
(u) 76ml (v) 722ml (w) 60ml (x) 5ml
5. (a) 4m (b) 3m (c) 12m (d) 114m
(e) 0·6m (f) 0·7m (g) 0·91m (h) 0·28m
(i) 52·3m (j) 28·71m (k) 10·09m (l) 33·22m
(m) 0·08m (n) 0·07m (o) 0·01m (p) 0·05m
6. (a) 700cm (b) 3600cm (c) 12000cm (d) 13400cm
(e) 57000cm (f) 2300cm (g) 1230cm (h) 906cm
(i) 640cm (j) 60cm (k) 205cm (l) 780cm
(m) 798cm (n) 400۰7cm (o) 9cm (p) 70cm
7. (a) 700cm (b) 360cm (c) 1020cm (d) 1140cm
(e) 57cm (f) 23cm (g) 12·3cm (h) 90·6cm
(i) 6cm (j) 2cm (k) 2·5cm (l) 7·8cm
(m) 0·7cm (n) 0·4cm (o) 0·2cm (p) 0·1cm
8. (a) 80mm (b) 30mm (c) 67mm (d) 69·8mm
(e) 3·4mm (f) 17·8mm (g) 25·9mm (h) 30·9mm
9. (a) 6km (b) 1·5km (c) 29km (d) 4·87km
(e) 0·536km (f) 0·65km (g) 0·021m (h) 0·007m
10. (a) 3000m (b) 12000m (c) 3800m (d) 4670m
(e) 216m (f) 640m (g) 370m (h) 17m
11. (a) 7m (b) 3·6m (c) 10·2m (d) 11·4m
(e) 0·57m (f) 0·23m (g) 0·123m (h) 0·906m
(i) 0·06m (j) 0·02m (k) 0·025m (l) 0·078m
(m) 0·007m (n) 0·004m (o) 0·002m (p) 0·001mm
12. (a) 9000mm (b) 2000mm (c) 3300mm (d) 5340mm
(e) 234mm (f) 780mm (g) 990mm (h) 9mm
13. (a) 7km (b) 1·5km (c) 2·3km (d) 0·567km
(e) 0·5361km (f) 0·0470km (g) 0·0066km (h) 0·0009km
14. (a) 200000cm (b) 2300000cm (c) 350000cm (d) 153000cm
(e) 33300cm (f) 67400cm (g) 55700cm (h) 4600cm
Pegasys 2013
Reading Tables
1. (a) £5.50 (b) £5 (c) £23
2. (a) £628 (b) £832.50 (c) £2061.50
3. (a) 19th
(b) Thursday (c) 11 nights (d) 7th
4. (a) 13km (b) 27km (c) 51km
5. (a) (i) 50p (ii) £9.60 (iii) £24 (iv) £7.35
(b) £4.50 for 50 copies; £4.40 for 55 copies so Jamie was correct (c) £1.80
6. (a) 38 (b) 41 (c) 36
7. (a) (i) 5 (ii) 8 (iii) 4
(b) 14 (c) £146.50
8. (a) 230 people (b) 24 (c) 167 (d) more people choose to cruise or any
acceptable comment
9. (a) £682.36 (b) £34.12 (c) £329.47 (d) £8000; 36 months,
without loan protection
(e) £10000 for 36 months (f) £15000 for 48 months
10. (a) £15 (b) 18·6% (c) 1·61%
(d) £4 or 4% (e) £7.50 (f) £6
11. (a) 16days
(b) (i) £4438 (ii) £8140 (iii) £8341 (iv) £2494
12. (a) £4348 (b) £2946 (c) £1730.40 (d) £1113
Interpreting statistical diagrams
1. (a) 6 (b) ready salted (c) 82 (d) roast chicken
(e) ready salted, salt & vinegar, prawn cocktail, cheese & onion, smoky bacon,
roast chicken
2. (a) Tuesday (b) Wednesday (c) 12
3. (a) 7 (b) 3 (c) 6 (d) 35
4. (a) (i) ½ (ii) ¼ (iii) 1/8 (iv)
1/8
(b) 300 (c) 150
5. (a) (i) ¼ (ii) ½ (iii) 1/20 (iv)
1/5
(b) action
Pegasys 2013
6. (a) (i) 1/10 (ii)
2/5 (iii)
3/10 (iv)
1/5
(b) walk (c) 12
7. (a) December (b) 6·5, 11 (c) 2·5
8. (a) time gets less (b) practice makes perfect
9. (a) 2·9 kg (b) 4·6, 5·7, 6·8 (c) 1·2 kg (d) 11 and 12
10. (a) 16 plants (b) 63cm (c) 56cm, 57cm, 59cm (d) ¼
11. (a) (b) £75
12. (a) 45 days (b) last year 28 days; this year 17 days
(c) Absence rate appears to have decreased since last year. or equivalent.
Interpret Statistics
1. (a)
(b) “Both boxes are very poor. Brighto is possibly the better of the two.” or equivalent.
2. (a) size 7 (b) mode 3. Yes. Mean = 48, median = 48
4. (a) 26, 25, no mode (b) below (c) 4, 25, 25 (d) above the mean
5. (a) 17000, 15000, 15000 (b) median
6. (a) 785 (b) 36110
7. (a) A: 2 teams of 14, 15, 16, 17, 18 B: 14, 14, 15, 16, 18 & 14, 15, 16, 16, 17
(b) No. Mean age = 16·2 8. mode (22) 9. (a) £21.22 (b) less than mean (just over half)
6 7 8 9
6 8 1 3 5 5 5 8 9 0 1 3 2
Cost of CD Player (£)
n = 13 7 4 represents £74
Number of Matches per box
n = 14
2
3
4
5
6
9
8 9
0 2 9 9
1 2 6 7 8
2 4
6 7 8 9 9
1 5 6 7 8
0 2 8
1
n = 14 4 8 represents 48 matches
Brighto Sparky
Pegasys 2013
Probability
1. (a) A (b) A (c) both same
(d) A (e) B (f) B - with reasons
2. (a) (i) 40 (ii) 40
(b) (i) 12 (ii) 4
(c) (i) 39 (ii) 36 (iii) 3
(d) (i) 28 (ii) 12 (iii) 4
3. (a) ¾ (b) 16
4. (a) 0·76 (b) 18